handbook of fourier analysis & its applicationsthe nonuniform discrete fourier transform and its...

[13:27 7/10/2008 5165-Marks-FM.tex] Job No: 5165 MARKS: Doing Qualitative Research Using Your Computer Page: iii 1–xxvii

Handbook of FourierAnalysis & Its Applications

Robert J. Marks II

2008

[13:28 15/10/2008 5165-marks-references.tex] Job No: 5165 MARKS: Doing Qualitative Research Using Your Computer Page: 680 680–744

15

References

A

[1] J.B. Abbiss, C. De Mol, and H.S. Dhadwal. Regularized iterative and non-iterative proceduresfor object restoration from experimental data. Opt. Acta, pp. 107–124, 1983.

[2] J.B. Abbiss, B.J. James, J.S. Bayley, and M.A. Fiddy. Super-resolution and neural computing.Proceedings SPIE, International Society Optical Engineering, pp. 100–106, 1988.

[3] Edwin A. Abbott. Flatland: A Romance of Many Dimensions. Dover, 2007. Originallypublished in 1884.

[4] Ray Abma and Nurul Kabir. 3D interpolation of irregular data with a POCS algorithm.Geophysics. Vol. 71(6), pp. E91–E97, 2006.

[5] M. Abramowitz and I.A. Stegun. Handbook of Mathematical Functions. Dover, New York,9th ed., 1964.

[6] L.D. Abreu. A q-sampling theorem related to the q-Hankel transform. Proceedings of theAmerican Mathematical Society, Vol. 133(4), pp. 1197–1203, 2005.

[7] Amir D. Aczel. The Mystery of the Aleph: Mathematics, the Kabbalah, and the HumanMind. Four Walls Eight Windows, 2000.

[8] H.C. Agarwal. Heat transfer in laminar flow between parallel plates at small Peclet numbers.Applied Sci. Res., Vol. 9, pp. 177–189, 1960.

[9] R. Agarwal, M. Bohner, and A. Peterson. Inequalities on time scales: A survey. MathematicalInequalities and Applications, Vol. 4(4), pp. 535–557, 2001.

[10] R. Agarwal, M. Bohner, D. O’Regan et al. Dynamic equations on time scales: a survey. Journalof Computational and Applied Mathematics, Vol. 141(1–2), pp. 1–26, 2002.

[11] T.H. Ahberg, E.N. Nilson, and T.L. Walsh. The Theory of Splines and Their Applications.Academic Press, New York, 1964.

[12] C.B. Ahn, J.H. Kim, and Z.H. Cho. High-speed spiral echo planar NMR imaging – I. IEEETransactions Medical Imaging, Vol. MI-5, pp. 2–7, 1986.

[13] S.T. Alexander. Fast Adaptive Filters: A Geometrical Approach. IEEE ASSP Magazine,pp. 18–28, 1986.

[14] Z. Alkachouh and M. G. Bellanger. Fast DCT-based spatial domain interpolation of blocks inimages. IEEE Transactions Image Processing., Vol. 9, No. 4. pp. 729–732, 2000.

[15] J.P. Allebach. Analysis of sampling pattern dependence in time-sequential sampling of spatio-temporal signals. Journal of the Optical Society America, Vol. 71, pp. 99–105, 1981.

[16] L.B.Almedia.An introduction to the angular Fourier transform. Proceedings IEEE InternationalConf. Acoust., Speech, Signal Process., Minneapolis, MN, 1993.

[17] L.B. Almeida. The fractional Fourier transform and time-frequency representations. IEEETransactions on Signal Processing. Vol. 42(11), pp. 3084–3091, 1994.

[18] L.B. Almeida, Product and Convolution Theorems for the Fractional Fourier Transform. IEEESignal Processing Letters, Vol. 4(1), pp. 15–17, 1997.

680


REFERENCES 681

[19] Oktay Altun. Gaurav Sharma, Mehmet U. Celik, and Mark F. Bocko. A set theoretic frameworkfor watermarking and its application to semifragile tamper detection. IEEE Transactions onInformation Forensics and Security. Vol. 1(4), pp. 479–492, 2006.

[20] M.Ancis and D.D. Giusto. Reconstruction of missing blocks in JPEG picture transmission. IEEEPacific Rim Conference, pp. 288–291, 1999.

[21] B. Andò, S. Baglio, S. Graziani and N. Pitrone. Threshold Error Reduction in LinearMeasurement Devices by Adding Noise Signal. Proceedings of the IEEE Instrumentation andMeasurements Technology Conference, St. Paul, Minnesota, pp. 18–21, 42–46, 1998.

[22] H.C. Andrews and C.L. Patterson. Singular value decompositions and digital image processing.IEEE Transactions Acoust., Speech, Signal Processing, pp. 26–53, 1976.

[23] K.Araki. Sampling and recovery formula in finite Hankel transform based on the minimum normprinciple. Transactions Institute Electron. Commun. Engineering Jpn., Vol. J68A, pp. 643–649,1985.

[24] F.Arago. Joseph Fourier, Biographies of Distinguished Scientific Men. London, pp. 242–286,1957.

[25] H. Arsenault. Diffraction theory of Fresnel zone plates. Journal of the Optical Society America,Vol. 58, p. 1536, 1968.

[26] H. Arsenault and A. Boivin. An axial form of the sampling theorem and its application to opticaldiffraction. Journal Applied Phys., Vol. 38, pp. 3988–3990, 1967.

[27] H. Arsenault and K. Chalasinska-Macukow. The solution to the phase retrieval problem usingthe sampling theorem. Optical Communication, Vol. 47, pp. 380–386, 1983.

[28] H. Arsenault and B. Genestar. Deconvolution of experimental data. Can. J. Phys., Vol. 49,pp. 1865–1868, 1971.

[29] H. Artes, F. Hlawatsch and G. Matz. Efficient POCS algorithms for deterministic blindequalization of time-varying channels. IEEE Global Telecommunications Conference, 2000.GLOBECOM ’00. Vol. 2,27, pp. 1031–1035, 2000.

[30] S. Chaturvedi, N. Arvind, Mukunda, et al. The sampling theorem and coherent state systems inquantum mechanics. Physica Scripta, Vol. 74(2), pp. 168–179, 2006.

[31] R.B. Ash. Information Theory. Interscience, New York, 1965.[32] J.L. Aravena. Recursive moving window DFT algorithm. IEEE Transactions Computers, Vol. 39,

pp. 145–151, 1990.[33] Nakhle H.Asmar. Partial Differential Equations and BoundaryValue Problems with Fourier

Series (2nd Edition). Prentice Hall, 2004.[34] C. Atzeni and L. Masotti. A new sampling procedure for the synthesis of linear transversal filters.

IEEE Transactions Aerospace & Electronic Systems, Vol. AES-7, pp. 662–670, 1971.[35] T. Auba and Y. Funahashi. The structure of all-pass matrices that satisfy directional interpolation

requirements. IEEE Transactions Automatic Control, Vol. 36, pp. 1485–1489, 1991.[36] T. Auba and Y. Funahashi. The structure of all-pass matrices that satisfy two-sided interpolation

requirements. IEEE Transactions Automatic Control, Vol. 36, pp. 1489–1493, 1991.[37] D.A. August and W.B. Levy. A simple spike train decoder inspired by the sampling theorem.

Neural Computation, Vol. 8(1), pp. 67–84, 1996.[38] Saint Augustine. DeGenesi ad Letteram, Book II.[39] L. Auslander and R. Tolimieri. Characterizing the radar ambiguity functions. IEEE Transactions

Information Theory, Vol. IT-30, pp. 832–836, 1984.

B[40] A. Bachl and W. Lukosz. Experiment on super-resolution imaging of a reduced object field.

Journal of the Optical Society America, Vol. 57, pp. 163–169, 1967.[41] Sonali Bagchi and Sanjit K. Mitra. The Nonuniform Discrete Fourier Transform and its

Applications in Signal Processing. Springer, 1998.[42] A.V. Balakrishnan. A note on the sampling principle for continuous signals. IRE Transactions

Information Theory, Vol. IT-3, pp. 143–146, 1957.[43] A.V. Balakrishnan. On the problem of time jitter in sampling. IRE Transactions Information

Theory, Vol. IT-8, pp. 226–236, 1962.


682 REFERENCES

[44] A.V. Balakrishnan. Essentially bandlimited stochastic processes. IEEE Transactions InformationTheory, Vol. IT-11, pp. 145–156, 1965.

[45] C. Bardaro, P.L. Butzer, R.L. Stens RL, et al. Approximation error of the Whittaker cardinalseries in terms of an averaged modulus of smoothness covering discontinuous signals. Journalof Mathematical Analysis and Applications, Vol. 316(1), pp. 269–306, 1 2006.

[46] I. Bar-David. An implicit sampling theorem for bounded bandlimited functions. Information &Control, Vol. 24, pp. 36–44, 1974.

[47] I. Bar-David. Sample functions of a Gaussian process cannot be recovered from their zerocrossings. IEEE Transactions Information Theory, Vol. IT-21, pp. 86–87, 1975.

[48] I. Bar-David. On the degradation of bandlimiting systems by sampling. IEEE TransactionsCommunications, Vol. COM-25, pp. 1050–1052, 1977.

[49] R. Barakat. Application of the sampling theorem to optical diffraction theory. Journal of theOptical Society America, Vol. 54, pp. 920–930, 1964.

[50] R. Barakat. Determination of the optical transfer function directly from the edge spread function.Journal of the Optical Society America, Vol. 55, pp. 1217–1221, 1965.

[51] R. Barakat. Nonlinear transformation of stochastic processes associated with Fourier transformsof bandlimited positive functions. International J. Contr., Vol. 14, No. 6, pp. 1159–1167,1971.

[52] R. Barakat. Note on a sampling expansion posed by O’Neill and Walther. Optical Communica-tion, Vol. 23, pp. 207–208, 1977.

[53] R. Barakat. Shannon numbers of diffraction images. Optical Communication, pp. 391–394,1982.

[54] R. Barakat and E. Blackman. Application of the Tichonov regularization algorithm to objectrestoration. Optical Communication, pp. 252–256, 1973.

[55] R. Barakat and A. Houston. Line spread and edge spread functions in the presence of off-axisaberrations. Journal of the Optical Society America, Vol. 55, pp. 1132–1135, 1965.

[56] R. Barakat and J.E. Cole III. Statistical properties of n random sinusoidal waves in additiveGaussian noise. Journal Sound and Vibration, Vol. 63, pp. 365–377, 1979.

[57] V. Bargmann, P. Butera, L. Girardello, and J.R. Klauder. On the completeness of the coherentstates, Rep. Math. Phys. 2, pp. 221–228, 1971.

[58] H.A. Barker. Synchronous sampling theorem for nonlinear systems. Electron. Letters, Vol. 5,p. 657, 1969.

[59] C.W. Barnes. Object restoration in a diffraction-limited imaging system. Journal of the OpticalSociety America, Vol. 56, pp. 575–578, 1966.

[60] H.O. Bartelt, K.H. Brenner, and A.W. Lohmann. The Wigner distribution function and its opticalproduction. Optical Communication Vol. 32, pp. 32–38, 1980.

[61] H.O. Bartelt and J. Jahns. Interferometry based on the Lau effect. Optical Communication,pp. 268–274, 1979.

[62] M.J. Bastiaans. A frequency-domain treatment of partial coherence. Opt. Acta, Vol. 24,pp. 261–274, 1977.

[63] M.J. Bastiaans. A generalized sampling theorem with application to computer-generatedtransparencies. Journal of the Optical Society America, Vol. 68, pp. 1658–1665, 1978.

[64] M.J. Bastiaans. The Wigner distribution function applied to optical signals and systems. OpticalCommunication, Vol. 25, pp. 26–30, 1978.

[65] M.J. Bastiaans. The Wigner distribution function and Hamilton’s characteristics of a geometrical-optical system. Optical Communication, Vol. 30, pp. 321–326, 1979.

[66] M.J. Bastiaans. Sampling theorem for the complex spectrogram, and Gabor’s expansion of asignal in Gaussian elementary signals, in 1980 International Optical Computing Conference,ed. W.T. Rhodes, Proceedings SPIE, Vol. 231, pp. 274–280, 1980 (also published in OpticalEngineering, Vol. 20, pp. 594–598, 1981).

[67] M.J. Bastiaans. The expansion of an optical signal into a discrete set of Gaussian beams. Optik,Vol. 57, pp. 95–102, 1980.

[68] M.J. Bastiaans. A sampling theorem for the complex spectrogram, and Gabor’s expansion of asignal in Gaussian elementary signals. Optical Engineering, Vol. 20, pp. 594–598, 1981.


REFERENCES 683

[69] M.J. Bastiaans. Gabor’s signal expansion and degrees of freedom of a signal. Opt. Acta, Vol. 29,pp. 1223–1229, 1982.

[70] M.J. Bastiaans. Optical generation of Gabor’s expansion coefficients for rastered signals.Opt. Acta, Vol. 29, pp. 1349–1357, 1982.

[71] M.J. Bastiaans. Signal description by means of a local frequency spectrum. Proceedings SPIE,International Society Optical Engineering, Vol. 373, pp. 49–62, 1981.

[72] M.J. Bastiaans. Gabor’s signal expansion and degrees of freedom of a signal. Opt. Acta, Vol. 29,pp. 1223–1229, 1982.

[73] M.J. Bastiaans. On the sliding-window representation in digital signal processing. IEEETransactions Acoust., Speech, Signal Processing Vol. ASSP-33, pp. 868–873, 1985.

[74] M.J. Bastiaans. Error reduction in two-dimensional pulse-area modulation, with application tocomputer-generated transparencies. 14th Congress of the International Commission for Optics,ed. H.H. Arsenault, Proceedings SPIE, Vol. 813, pp. 341–342, 1987.

[75] M.J. Bastiaans. Error reduction in one-dimensional pulse-area modulation, with applicationto computer-generated transparencies. Journal of the Optical Society America A, Vol. 4,pp. 1879–1886, 1987.

[76] M.J. Bastiaans. Local-frequency descriptions of optical signals and systems. EUT Report88–E–191 (Faculty of Electrical Engineering, Eindhoven University of Technology,Eindhoven, Netherlands, 1988).

[77] M.J. Bastiaans. Gabor’s signal expansion applied to partially coherent light. OpticalCommunication, Vol. 86, pp. 14–18, 1991.

[78] M.J. Bastiaans. On the design of computer-generated transparencies based on area modulationof a regular array of pulses. Optik, Vol. 88, pp. 126–132, 1991.

[79] M.J. Bastiaans. Second-order moments of the Wigner distribution function in first-order opticalsystems. Optik, Vol. 88, pp. 163–168, 1991.

[80] M.J. Bastiaans, M.A. Machado, and L.M. Narducci. The Wigner distribution function andits applications in optics. Optics in Four Dimensions-1980, AIP Conf. Proceedings 65, eds.(American Institute of Physics, New York, 1980), pp. 292–312, 1980.

[81] Sankar Basu and Bernard C. Levy. Multidimensional Filter Banks and Wavelets: BasicTheory and Cosine Modulated Filter Banks. Springer, 1996.

[82] J.S. Bayley and M.A. Fiddy. On the use of the Hopfield model for optical pattern recognition.Optical Communication, pp. 105–110, 1987.

[83] M.G. Beaty and M.M. Dodson. The Whittaker-Kotel’nikov-Shannon theorem, spectral translatesand Plancherel’s formula. Journal of Fourier Analysis and Applications, Vol. 10(2), pp. 179–199,2004.

[84] Reinhard Beer. Remote Sensing by Fourier Transform Spectrometry. John Wiley & Sons,1992.

[85] A.H. Beiler. Ch. 11 in Recreations in the Theory of Numbers: The Queen of MathematicsEntertains. New York: Dover, 1966.

[86] G.A. Bekey and R. Tomovic. Sensitivity of discrete systems to variation of sampling interval.IEEE Transactions Automatic Control, Vol. AC-11, pp. 284–287, 1966.

[87] B.W. Bell and C.L. Koliopoulos. Moiré topography, sampling theory, and charged-coupleddevices. Optical Letters, Vol. 9, pp. 171–173, 1984.

[88] D.A. Bell. The Sampling Theorem. International Journal of Electrical Engineering, Vol. 18(2),pp. 175–175, 1981.

[89] E.T. Bell. Men of Mathematics. Touchstone (Reissue edition) 1986.[90] V.K. Belov and S.N. Grishkin. Digital bandpass filters with nonunform sampling.

Priborostroemie, Vol. 23, No. 3 (in Russian), pp. 3–7, 1980.[91] V.I. Belyayev. Processing and theoretical analysis of oceanographic observations. Translation

from Russian JPRS 6080, 1973.[92] John J. Benedetto and Paulo J.S.G. Ferreira. Modern SamplingTheory. by (Hardcover - Feb. 16,

2001) Birkhäuser user Boston, 2001.[93] J.J. Benedetto and Ahmed I. Zayed (Editors). Sampling, Wavelets, and Tomography. Pub.

Date: December 2003 Publisher: Birkhäuser user Verlag.


684 REFERENCES

[94] M. Bendinelli, A. Consortini, L. Ronchi, and R.B. Frieden. Degrees of freedom andeigenfunctions of the noisy image. Journal of the Optical Society America, Vol. 64,pp. 1498–1502, 1974.

[95] M. Bennett, et al. Filtering of ultrasound echo signals with the fractional Fourier transform.Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicineand Biology Society, Vol. 1(17–21), pp. 882–885, 2003.

[96] N. Benvenuto and G.L. Pierobin. Extension of the sampling theorem to exponentially decayingcausal functions. IEEE Transactions on Signal Processing, Vol. 39(1), pp. 189–190, 1991.

[97] N. Benvenuto, L. Franks, F. Hill. Realization of Finite Impulse Response Filters UsingCoefficients +1, 0, and −1. IEEE Transactions on Communications, Oct 1985, Vol.33, Issue10, pp. 1117–1125.

[98] E.M. Bernat, W.J. Williams, and W.J. Gehring. Decomposing ERP time-frequency energy usingPCA. Clinical Neurophysiology. Vol. 116(6), pp. 1314–1334, 2005.

[99] M. Bertero. Linear inverse and ill-posed problems. In P.W. Hawkes, editor, Advances inElectronics and Electron Physics. Academic Press, New York, 1989.

[100] M. Bertero, P. Boccacci, and E.R. Pike. Resolution in diffraction-limited imaging, a singularvalue analysis. II. The case of incoherent illumination. Opt. Acta, pp. 1599–1611, 1982.

[101] M. Bertero, C. de Mol, E.R. Pike, and J.G. Walker. Resolution in diffraction-limited imaging,a singular value analysis. IV. The case of uncertain localization or non-uniform illumination ofthe object. Opt. Acta, pp. 923–946, 1984.

[102] M. Bertero, C. De Mol, and E.R. Pike. Analytic inversion formula for confocal scanningmicroscopy. Journal of the Optical Society America A, pp. 1748–1750, 1987.

[103] M. Bertero, C. De Mol, and G.A. Viano. Restoration of optical objects using regularization.Optics Letters, pp. 51–53, 1978.

[104] M. Bertero, C. De Mol, and G.A. Viano. On the problems of object restoration and imageextrapolation in optics. Journal Math. Phys., pp. 509–521, 1979.

[105] M. Bertero and E.R. Pike. Resolution in diffraction-limited imaging, a singular value analysis.I. The case of coherent illumination. Opt. Acta, pp. 727–746, 1982.

[106] M. Bertero and E.R. Pike. Exponential sampling method for Laplace and other dilationallyinvariant transforms: I. Singular system analysis. Inverse Problems, pp. 1–20, 1991.

[107] M. Bertero and E.R. Pike. Exponential sampling method for Laplace and other dilationallyinvariant transforms: II. Examples in photon correlation spectroscopy and Fraunhoferdiffraction. Inverse Problems, pp. 21–41, 1991.

[108] A.S. Besicovitch. Almost Periodic Functions. Wiley Interscience, New York, 1968.[109] F.J. Beutler. Sampling theorems and bases in a Hilbert space. Information & Control, Vol. 4,

pp. 97–117, 1961.[110] F.J. Beutler. Error-free recovery of signals from irregularly spaced samples. SIAM Review,

Vol. 8, No. 3, pp. 328–335, 1966.[111] F.J. Beutler. Alias-free randomly timed sampling of stochastic processes. IEEE Transactions

on Information Theory, Vol. IT–16, pp. 147–152, 1970.[112] F.J. Beutler. Recovery of randomly sampled signals by simple interpolators. Information &

Control, Vol. 26, No. 4, pp. 312–340, 1974.[113] F.J. Beutler. On the truncation error of the cardinal sampling expansion. IEEE Transactions

Information Theory, Vol. IT-22, pp. 568–573, 1976.[114] F.J. Beutler and D.A. Leneman. Random sampling of random processes: stationary point

processes. Information & Control, Vol. 9, pp. 325–344, 1966.[115] F.J. Beutler and D.A. Leneman. The theory of stationary point processes. Acta Math, Vol. 116,

pp. 159–197, September 1966.[116] V. Bhaskaran and K. Konstantinides. Image and Video Compression Standards, Kluwer,

1995.[117] Arun K. Bhattacharyya. Phased Array Antennas: Floquet Analysis, Synthesis, BFNs and

Active Array Systems. Wiley-Interscience, 2006.[118] A.M. Bianchi and L.T. Mainardi and S. Cerutti. Time-frequency analysis of biomedical signals.

Transactions of the Institute of Measurement and Control, Vol. 22(3), pp. 215–230, 2000.


REFERENCES 685

[119] H.S. Black. Modulation Theory. Van Nostrand, New York, 1953.[120] R.B. Blackman and J.W. Tukey. The measurement of power spectra from the point of view of

communications engineering. Bell Systems Tech. J., Vol. 37, p. 217, 1958.[121] W.E. Blash. Establishing proper system parameters for digitally sampling a continuous scanning

spectrometer. Applied Spectroscopy., Vol. 30, pp. 287–289, 1976.[122] V. Blazek. Sampling theorem and the number of degrees of freedom of an image. Optical

Communication, Vol. 11, pp. 144–147, 1974.[123] E.M. Bliss. Watch out for hidden pitfalls in signal sampling. Electron. Engineering, Vol. 45,

pp. 59–61, 1973.[124] Peter Bloomfield. Fourier Analysis of Time Series: An Introduction.Wiley-Interscience,

2000.[125] R.P. Boas, Jr. Entire Functions. Academic Press, New York, 1954.[126] R.P. Boas, Jr. Summation formulas and bandlimited signals. Tohoku Math. J., Vol. 24,

pp. 121–125, 1972.[127] Salomon Bochner and Komaravolu Chandrasekharan. Fourier Transforms. Princeton

University Press, 1949.[128] M. Bohner and A. Peterson. Dynamic Equations on Time Scales: An Introduction with

Applications. Birkhauser, Boston, 2001.[129] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkhäuser, Boston, 2001.[130] H. Bohr. Almost Periodic Functions. Wiley Interscience, New York, 1968.[131] A. Boivin and C. Deckers. A new sampling theorem for the complex degree of coherence for

reconstruction of a luminous isotropic source. Optical Communication, Vol. 26, pp. 144–147,1978.

[132] P. Bonato, S.H. Roy, M. Knaflitz et al. Time-frequencyparameters of the surface myoelectricsignal for assessing muscle fatigue during cyclic dynamic contractions. IEEE Transactions ofBiomedical Engineering. Vol. 48(7), pp. 745–753, 2001.

[133] F.E. Bond and C.R. Cahn. On sampling the zeros of bandwidth limited signals. IRE TransactionsInformation Theory, Vol. IT-4, pp. 110–113, 1958.

[134] F.E. Bond, C.R. Cahn, and J.C. Hancock. A relation between zero crossings and Fouriercoefficients for bandlimited functions. IRE Transactions Information Theory, Vol. IT-6,pp. 51–55, 1960.

[135] C. de Boor. A Practical Guide to Splines. Springer-Verlag, New York, 1978.[136] E. Borel. Sur l’interpolation. C.R. Acad. Sci. Paris, Vol. 124, pp. 673–676, 1877.[137] E. Borel. Mémoire sur les séries divergentes. Ann. Ecole Norm. Sup., Vol. 3, pp. 9–131, 1899.[138] E. Borel. La divergence de la formule de Lagrange a été établie également. In Leçons sur les

fonctions de variables réelles et les développements en séries de polynômes. Gauthier-Villars,Paris, 1905, pp. 74–79.

[139] M. Born and E. Wolf. Principles of Optics. Pergamon Press, Oxford, 1980.[140] T. Bortfeld, J. Burkelbach, R. Boesecks, and W. Schlegal. Methods of image reconstruction

from projections applied to conformation radiotherapy. Phys. Med. Biol., Vol. 35, pp. 1423–34,1990.

[141] Robert L. Boylestad, and Louis Nashelsky. Electronic Devices and Circuit Theory (8thEdition), Prentice Hall, 2001.

[142] A. Boumenir et al. Eigenvalues of periodic Sturm-Liouville problems by the Shannon-Whittaker sampling theorem. Mathematics of Computation, Vol. 68(227), pp. 1057–1066,1999.

[143] F. Bouzeffour. A q-sampling theorem and product formula for continuous q-Jacobi functions.Proceedings of the American Mathematical Society, Vol. 135(7), pp. 2131–2139, 2007.

[144] G.E.T. Box and G.M. Jenkins. Time Series Analysis. Forecasting and Control (revisededition). Holden-Day, San Francisco, 1976.

[145] G.D. Boyd and J.P. Gordon. Confocal multimode resonator for millimeter through opticalwavelength masers. Bell Systems Tech. J., pp. 489–508, 1961.

[146] G.D. Boyd and H. Kogelnik. Generalized confocal resonator theory. Bell Systems Tech. J.,pp. 1347–1369, 1962.


686 REFERENCES

[147] G.R. Boyer. Realization d’un filtrage super-resolvant. Opt. Acta, pp. 807–816, 1983.[148] Ronald Newbold Bracewell. The Fourier Transform and its Applications, McGraw-Hill,

1965.[149] Ronald Newbold Bracewell. The Fourier Transform and its Applications, 2nd edition,

Revised. McGraw-Hill, New York, 1986.[150] Ronald Newbold Bracewell. The Hartley Transform. Oxford University Press, New York, 1986.[151] Ronald Newbold Bracewell. Fourier Analysis and Imaging. Plenum Publishing Corporation,

2004.[152] A. Brahme. Optimization of stationary and moving beam radiation therapy techniques.

Radiother. Oncol., 12 pp. 129–140, 1988.[153] Luca Brandolini, Leonardo Colzani,Alex Iosevich, and Giancarlo Travaglini. FourierAnalysis

and Convexity. Birkhäuser Boston, 2004.[154] David Brandwood. Fourier Transforms in Radar and Signal Processing. Artech House, 2003.[155] H. Bray, K. McCormick, and R.O. Wells et al. Wavelet variations on the Shannon sampling

theorem. Biosystems, Vol. 34(1–3), pp. 249–257, 1995.[156] L.M. Bregman. Finding the common point of convex sets by the method of successive

projections. Dokl. Akad. Nauk. USSR, Vol. 162, No. 3, pp. 487–490, 1965.[157] P. Bremer and J.C. Hart. A sampling theorem for MLS surfaces. Proceedings Eurographics/

IEEE VGTC Symposium on Point-Based Graphics, pp. 47–54.[158] Hans Bremermann. Distributions, Complex Variables, and Fourier transforms. Addison-

Wesley, 1965.[159] William L. Briggs and Van Emden Henson. The DFT: An Owners’ Manual for the Discrete

Fourier Transform. Society for Industrial Mathematics, 1987.[160] E.O. Brigham. The Fast Fourier Transform. Prentice-Hall, Englewood Cliffs, NJ, 1974.[161] E.O. Brigham. Fast Fourier Transform and Its Applications. Prentice Hall,1988.[162] L. Brillouin. Science and Information Theory. Academic Press, New York, 1962.[163] B.C. Brookes. Sampling theorem for finite discrete distributions. Journal of Documentation,

Vol. 31(1), pp. 26–35, 1975.[164] Eli Brookner. Practical Phased Array Antenna Systems. Artech House Publishers, 1991.[165] J.L. Brown, Jr. Anharmonic approximation and bandlimited signals. Information & Control,

Vol. 10, pp. 409–418, 1967.[166] J.L. Brown, Jr. On the error in reconstructing a non-bandlimited function by means of the

bandpass sampling theorem. Journal Math. Anal. Applied, Vol. 18, pp. 75–84, 1967; Erratum,Vol. 21, p. 699, 1968.

[167] J.L. Brown, Jr. A least upper bound for aliasing error. IEEE Transactions Automatic Control,Vol. AC-13, pp. 754–755, 1968.

[168] J.L. Brown, Jr. Sampling theorem for finite energy signals. IRE Transactions on InformationTheory, Vol. IT-14, pp. 818–819, 1968.

[169] J.L. Brown, Jr. Bounds for truncation error in sampling expansions of bandlimited signals. IRETransactions Information Theory, Vol. IT-15, pp. 669–671, 1969.

[170] J.L. Brown, Jr. Truncation error for bandlimited random processes. Inform. Sci., Vol. 1,pp. 261–272, 1969.

[171] J.L. Brown, Jr. Uniform linear prediction of bandlimited processes from past samples. IEEETransactions Information Theory, Vol. IT-18, pp. 662–664, 1972.

[172] J.L. Brown, Jr. On mean-square aliasing error in the cardinal series expansion of randomprocesses. IEEE Transactions Information Theory, Vol. IT-24, pp. 254–256, 1978.

[173] J.L. Brown, Jr. Comments on energy processing techniques for stress wave emission signals.Journal Acoust. Society America, Vol. 67, p. 717, 1980.

[174] J.L. Brown, Jr. First-order sampling of bandpass signals: a new approach. IEEE TransactionsInformation Theory, Vol. IT-26, pp. 613–615, 1980.

[175] J.L. Brown, Jr. Sampling bandlimited periodic signals – an application of the DFT. IEEETransactions Education, Vol. E-23, pp. 205–206, 1980.

[176] J.L. Brown, Jr. A simplified approach to optimum quadrature sampling. Journal Acoust. SocietyAmerica, Vol. 67, pp. 1659–1662, 1980.


REFERENCES 687

[177] J.L. Brown, Jr. Multi-channel sampling of low-pass signals. IEEE Transactions Circuits &Systems, Vol. CAS-28, pp. 101–106, 1981.

[178] J.L. Brown, Jr. Cauchy and polar-sampling theorems. Journal of the Optical Society America A,Vol. 1, pp. 1054–1056, 1984.

[179] J.L. Brown, Jr. An RKHS analysis of sampling theorems for harmonic-limited signals. IEEETransactions Acoust., Speech, Signal Processing, Vol. ASSP-33, pp. 437–440, 1985.

[180] J.L. Brown, Jr. Sampling expansions for multiband signals. IEEE Transactions Acoust., Speech,Signal Processing, Vol. ASSP-33, pp. 312–315, 1985.

[181] J.L. Brown, Jr. On the prediction of bandlimited signal from past samples. Proceedings IEEE,Vol. 74, pp. 1596–1598, 1986.

[182] J.L. Brown, Jr. and O. Morean. Robust prediction of bandlimited signals from past samples.IEEE Transactions Information Theory, Vol. IT-32, pp. 410–412, 1986.

[183] J.L. Brown, Jr. Sampling reconstruction of n-dimensional bandlimited images after multilinearfiltering. IEEE Transactions Circuits & Systems, Vol. CAS-36, pp. 1035–1038, 1989.

[184] J.L. Brown. Summation of certain series using the Shannon sampling theorem. IEEETransactions on Education, Vol. 33(4), pp. 337–340, 1990.

[185] W.M. Brown. Fourier’s integral. Proceedings Edinburgh Math. Society, Vol. 34, pp. 3–10,1915–1916.

[186] W.M. Brown. On a class of factorial series. Proceedings London Math. Society, Vol. 2,pp. 149–171, 1924.

[187] W.M. Brown. Optimum prefiltering of sampled data. IRE Transactions Information Theory,Vol. IT-7, pp. 269–270, 1961.

[188] W.M. Brown. Sampling with random jitter. Journal SIAM, Vol. 2, pp. 460–473, 1961.[189] N.G. de Bruijn. A theory of generalized functions, with applications to Wigner distribution and

Weyl correspondence. Nieuw Arch. Wiskunde (3), Vol. 21, 205–280, 1973.[190] O. Bryngdahl. Image formation using self-imaging techniques. Journal of the Optical Society

America, Vol. 63, pp. 416–419, 1973.[191] O. Bryngdahl and F. Wyrowski. Digital holography. Computer generated holograms. In

newblock Progress in Optics, North-Holland, Amsterdam, pp. 1–86, 1990.[192] G.J. Buck and J.J. Gustincic. Resolution limitations of a finite aperture. IEEE Transactions

Antennas & Propagation, Vol. AP-15, pp. 376–381, 1967.[193] Aram Budak. Passive and Active Network Analysis and Synthesis, Waveland Press, 1991.[194] Y.G. Bulychev and I.V. Burlai. Repeated differentiation of finite functions with the use of

the sampling theorem in problems of control, estimation, and identification. Automation andRemote Control, Vol. 57(4), Part 1, pp. 499–509, 1996.

[195] J. Bures, P. Meyer, and G. Fernandez. Reconstitution d’un profil d’eclairement echantillonnepar une legne de microphotodiodes. Optical Communication, pp. 39–44, 1979.

[196] Tilman Butz. Fourier Transformation for Pedestrians (Fourier Series). Springer, 2005.[197] P.L. Butzer. A survey of the Whittaker-Shannon sampling theorem and some of its extensions.

Journal Math. Res. Exposition, Vol. 3, pp. 185–212, 1983.[198] P.L. Butzer. The Shannon sampling theorem and some of its generalizations. An Overview. in

Constructive Function Theory, Proceedings Conf. Varna, Bulgaria, June 1–5, 1981; Bl. Sendovet al., eds., Publishing House Bulgarian Academy of Science., Sofia, pp. 258–274, 1983.

[199] P.L. Butzer. Some recent applications of functional analysis to approximation theory. (Proc.Euler Colloquium Berlin, May 1983; Eds: E. Knobloch et al). In: Zum Werk Leonhard Eulers.Birkhäuser, Basel, pp. 133–155, 1984.

[200] P.L. Butzer and W. Engels. Dyadic calculus and sampling theorems for functions withmultidimensional domain, I. General theory. Information & Control, Vol. 52, pp. 333–351,1982.

[201] P.L. Butzer and W. Engels. Dyadic calculus and sampling theorems for functions withmultidimensional domain, II. Applications to dyadic sampling representations. Information &Control, Vol. 52, pp. 352–363, 1982.

[202] P.L. Butzer and W. Engels. On the implementation of the Shannon sampling series forbandlimited signals. IEEE Transactions Information Theory, Vol. IT-29, pp. 314–318, 1983.


688 REFERENCES

[203] P.L. Butzer, W. Engels, S. Ries, and R.L. Stens. The Shannon sampling series and thereconstruction of signals in terms of linear, quadratic and cubic splines. SIAM J. Applied Math.,Vol. 46, pp. 299–323, 1986.

[204] P.L. Butzer, W. Engels, and U. Scheben. Magnitude of the truncation error in samplingexpansions of bandlimited signals. IEEE Transactions Acoust., Speech, Signal Processing.ASSP-30, pp. 906–912, 1982.

[205] P.L. Butzer and G. Hinsen. Reconstruction of bounded signals from pseudo-periodic irregularlyspaced samples. Signal Processing, Vol. 17, pp. 1–17, 1988.

[206] P.L. Butzer and G. Hinsen. Two-dimensional nonuniform sampling expansions – an iterativeapproach I, II. Applied Anal., Vol. 32, pp. 53–85, 1989.

[207] P.L. Butzer and C. Markett. The Poisson summation formula for orthogonal systems. InAnniversary Volume on Approximation Theory and Functional Analysis (Proceedings Conf.Math. Res. Institute Oberwolfach, Black Forest; Eds. Butzer, Stens, Nagy) Birkhäuser VerlagBasel - Stuttgart - Boston, = ISNM Vol. 65, pp. 595–601, 1984.

[208] P.L. Butzer and R.J. Nessel. Contributions to the theory of saturation for singular integrals inseveral variables I. General theory. Nederland Akad. Wetensch. Proceedings Ser. A, Vol. 69 andIndag. Math., Vol. 28, pp. 515–531, 1966.

[209] P.L. Butzer and R.J. Nessel. Fourier Analysis and Approximation Vol. I: One-DimensionalTheory. Birkhäuser Verlag, Basel, Academic Press, New York, 1971.

[210] P.L. Butzer, S. Ries, and R.L. Stens. The Whittaker-Shannon sampling theorem, relatedtheorems and extensions; a survey. In Proceedings JIEEEC ’83 (Proceedings Jordan -International Electrical and Electronic Engineering Conference, Amman, Jordan), pp. 50–56,1983.

[211] P.L. Butzer, S. Ries, and R.L. Stens. Shannon’s sampling theorem, Cauchy’s integral formulaand related results. In Anniversary Volume on Approximation Theory and Functional Analysis(Proceedings Conf. Math. Res. Institute Oberwolfach, Black Forest) Eds. Butzer Stens, andNagy Basel - Stuttgart - Boston: Birkhäuser Verlag = ISNM Vol. 65, pp. 363–377, 1984.

[212] P.L. Butzer, S. Ries, and R.L. Stens. Approximation of continuous and discontinuous functionsby generalized sampling series. Journal Approx. Theory, Vol. 50, pp. 25–39, 1987.

[213] P.L. Butzer, M. Schmidt, E.L. Stark, and L. Vogt. Central factorial numbers; their mainproperties and some applications. Num. Funct. Anal. Optim. Vol. 10, pp. 419–488, 1989.

[214] P.L. Butzer and M. Schmidt. Central factorial numbers and their role in finite difference calculusand approximation. Proceedings Conf. on Approximation Theory, Kecskemét, Hungary.Colloquia Mathematica Societatis János Bolyai, 1990.

[215] P.L. Butzer and W. Splettstößer. Approximation und Interpolation durch verallgemeinerteAbtastsummen. Forschungsberichte No. 2515, Landes Nordrhein-Westfalen, Köln-Opladen,1977.

[216] P.L. Butzer and W. Splettstößer. A sampling theorem for duration-limited functions with errorestimates. Information & Control, Vol. 34, pp. 55–65, 1977.

[217] P.L. Butzer and W. Splettstößer. Sampling principle for duration-limited signals and dyadicWalsh analysis. Inform. Sci., Vol. 14, pp. 93–106, 1978.

[218] P.L. Butzer and W. Splettstößer. On quantization, truncation and jitter errors in the samplingtheorem and its generalizations. Signal Processing, Vol. 2, pp. 101–102, 1980.

[219] P.L. Butzer, W. Splettstößer, and R.L. Stens. The sampling theorem and linear prediction insignal analysis. Jahresber. Deutsch Math.–Verein. Vol. 90, pp. 1–70, 1988.

[220] P.L. Butzer and R.L. Stens. Index of Papers on Signal Theory: 1972–1989. Lehrstuhl A fürMathematik, Aachen University of Technology, Aachen, Germany, 1990.

[221] P.L. Butzer and R.L. Stens. The Euler-Maclaurin summation formula, the sampling theorem,and approximate integration over the real axis. Linear Algebra Applications, Vol. 52/53,pp. 141–155, 1983.

[222] P.L. Butzer and R.L. Stens. The Poisson summation formula, Whittaker’s cardinal series andapproximate integration. In Proceedings Second Edmonton Conference on ApproximationTheory (Eds., Z. Ditzian, et al.) American Math. Society Providence, Rhode Island:=CanadianMath Society Proceedings, Vol. 3, pp. 19–36, 1983.


REFERENCES 689

[223] P.L. Butzer and R.L. Stens. A modification of the Whittaker-Kotelnikov-Shannon samplingseries. Aequationés Math., Vol. 28, pp. 305–311, 1985.

[224] P.L. Butzer and R.L. Stens. Prediction of non-bandlimited signals from past samples in termsof splines of low degree. Math. Nachr., Vol. 132, pp. 115–130, 1987.

[225] P.L. Butzer and R.L. Stens. Linear prediction in terms of samples from the past; an overview.In Numerical Methods and Approximation Theory III (Proceedings Conf. on NumericalMethods and Approximation Theory), Nis 18.–21.8.1987; Ed. G.V. Milovanovic, Faculty ofElectronic Engineering, University of Nis, Yugoslavia, 1988, pp. 1–22.

[226] P.L. Butzer and R.L. Stens. Sampling theory for not necessarily bandlimited functions; anhistorical overview. SIAM Review, Vol. 34, pp. 40–53, 1992.

[227] P.L. Butzer, R.L. Stens, and M. Wehrens. The continuous Legendre transform, its inversetransform and applications. International J. Math. Sci., Vol. 3, pp. 47–67, 1980.

[228] P.L. Butzer and H.J. Wagner. Walsh-Fourier series and the concept of a derivative. ApplicableAnalysis, Vol. 3, pp. 29–46, 1973.

[229] P.L. Butzer and H.J. Wagner. On dyadic analysis based on the pointwise dyadic derivative.Analysis Math., Vol. 1, pp. 171–196, 1975.

[230] P.L. Butzer, J.R. Higgins, and R.L. Stens. Classical and approximate sampling theorems; studiesin the L-P(R) and the uniform norm. Journal ofApproximationTheory,Vol. 137(2), pp. 250–263,2005.

[231] A. Buzo, A.H. Gray Jr., R.M. Gray, and J.D. Markel. Speech coding based uponvector quantization. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-28,pp. 562–574, 1980.

[232] A. Buzo, F. Kuhlmann, and C. Blas. Rate distortion bounds for quotient-based distortions withapplications to Itakura-Saito distortion measures. IEEE Transactions Inform. Theory,Vol. IT-32,pp. 141–147, 1986.

[233] William E. Byerly. An Elementary Treatise on Fourier’s Series and Spherical, Cylindrical,and Ellipsoidal Harmonics. Ginn & Co, Boston, 1933.

C[234] J. Cadzow. An extrapolation procedure for bandlimited signals. IEEE Transactions Acoust.,

Speech, Signal Processing, Vol. ASSP-27, pp. 4–12, 1979.[235] D. Cahana and H. Stark. Bandlimited image extrapolation with faster convergence. Applied

Optics, pp. 2780–2786, 1981.[236] G. Calvagio and D. Munson, Jr. New results on Yen’s approach to interpolation from

nonuniformly spaced samples. Proceedings IASSP, pp. 1533–1538, 1990.[237] S. Cambanis and M.K. Habib. Finite sampling approximation for non-bandlimited signals.

IEEE Transactions Information Theory, Vol. IT-28, pp. 67–73, 1982.[238] S. Cambanis and E. Masry. Truncation error bounds for the cardinal sampling expansion

of bandlimited signals. IEEE Transactions Information Theory, Vol. IT-28, pp. 605–612,1982.

[239] L.L. Campbell. A comparison of the sampling theorems of Kramer and Whittaker. JournalSIAM, Vol. 12, pp. 117–130, 1964.

[240] L.L. Campbell. Sampling theorem for the Fourier transform of a distribution with boundedsupport. SIAM J. Applied Math., Vol. 16, pp. 626–636, 1968.

[241] L.L. Campbell. Further results on a series representation related to the sampling theorem. SignalProcessing, Vol. 9, pp. 225–231, 1985.

[242] C. Candan, M.A. Kutay, and H.M. Ozaktas. The discrete fractional Fourier transform. IEEETransactions on Signal Processing, Vol. 48(5), pp. 1329–1337, 2000.

[243] K.G. Canfield, and D.L. Jones. Implementing time-frequency representations for non-Cohenclasses. 1993 Conference Record of The Twenty-Seventh Asilomar Conference on Signals,Systems and Computers, Vol. 2, pp. 1464–1468, 1993.

[244] George Cantor and Philip E.B. Jourdain. Contributions to the Founding of the Theory ofTransfinite Numbers. Cosimo Classics, 2007.


690 REFERENCES

[245] Gianfranco Cariolaro, Tomaso Erseghe, Peter Kraniauskas, and Nicola Laurenti. Multiplicityof Fractional Fourier Transforms and their Relationships. IEEE Transactions on SignalProcessing, Vol. 48(1), pp. 227–241, 2000.

[246] A.B. Carlson. Communications Systems, An Introduction to Signals and Noise in ElectricalCommunication, 2nd Ed. McGraw-Hill, New York, 1975.

[247] H.S. Carslaw. Introduction to the Theory of Fourier’s Series and Integrals. MichiganHistorical Reprint Series. Scholarly Publishing Office, University of Michigan, 2005.

[248] W.H. Carter and E. Wolf. Coherence and radiometry with quasihomogeneous sources. Journalof the Optical Society America Vol. 67, pp. 785–796, 1977.

[249] D. Casasent. Optical signal processing. In Optical Data Processing, D. Casasent, editor,Springer-Verlag, Berlin, pp. 241–282, 1978.

[250] Manuel F. Catedra, Rafael F. Torres, Emilio Gago, and Jose Basterrechea. CG-FFT Method:Application of Signal Processing Techniques to Electromagnetics. Artech House, 1994.

[251] W.T. Cathey, B.R. Frieden, W.T. Rhodes, and C.K. Rushforth. Image gathering and processingfor enhanced resolution. Journal of the Optical Society America A, pp. 241–250, 1984.

[252] A.L. Cauchy. Memoire sur diverses formules d’analyser, Comptes Rendus,Vol. 12, pp. 283–298,1841.

[253] H.J. Caulfield. Wavefront sampling in holography. Proceedings IEEE, Vol. 57, pp. 2082–2083,1969.

[254] H.J. Caulfield. Correction of image distortion arising from nonuniform sampling. ProceedingsIEEE, Vol. 58, p. 319, 1970.

[255] G. Cesini, P. Di Filippo, G. Lucarini, G. Guattari, and P. Pierpaoli. The use of charge-coupleddevices for automatic processing of interferograms. Journal of the Optical, pp. 99–103, 1981.

[256] G. Cesini, G. Guattari, G. Lucarini, and C. Palma.An iterative method for restoring noisy images.Opt. Acta, pp. 501–508, 1978.

[257] A.E. Cetin, H. Ozaktus, and H.M. Ozaktus. Signal recovery from partial fractional Fouriertransform information. First International Symposium on Control, Communications and SignalProcessing, pp. 217–220, 2004.

[258] J. Cezanne and A. Papoulis. The use of modulated splines for the reconstruction ofbandlimited signals. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP–36,No. 9, pp. 1521–1525, 1988.

[259] K. Chalasinkamacukow, H.H.Arsenault. Solution to the phase-retrieval problem using the sam-pling theorem. Journal of the Optical Society of America, Vol. 73(12), pp. 1875–1875, 1983.

[260] K. Chalasinska-Macukow and H.H. Arsenault. Fast iterative solution to exact equations for thetwo-dimensional phase-retrieval problem. Journal of the Optical Society America A, Vol. 2,pp. 46–50, 1985.

[261] D.C. Champeney. Fourier Transforms and their Physical Applications. Academic Press,1973.

[262] D.C. Champeney. Fourier Transforms in Physics. Taylor & Francis, 1985.[263] C. Chamzas and Wen Xu. An improved version of Papoulis-Gerchberg algorithm on

band-limited extrapolation.IEEE Transactions on Acoustics, Speech, and Signal Processing,Vol. 32(2), pp. 437–440, 1984.

[264] S.S. Chang. Optimum transmission of a continuous signal over a sampled data link. AIEETransactions, Vol. 79, Pt. II (Applications and Industry), pp. 538–542, 1961.

[265] I.J. Chant and L.M. Hastie, A comparison of the stability of stationary and nonstationary mag-netotelluric analysis methods. International Geophysical Journal, Vol. 115(3), pp. 1143–1147,1993.

[266] J.I. Chargin and V.P. Iakovlev. Finite Functions in Physics and Technology. Nauka, Moscow,1971.

[267] D.B. Chase and J.F. Rabolt. Fourier Transform Raman Spectroscopy: From Concept toExperiment. Academic 1994.

[268] P. Chavel and S. Lowenthal. Noise and coherence in optical image processing. I. The Calliereffect and its influence on image contrast. Journal of the Optical Society America, Vol. 68,pp. 559–568, 1978.


REFERENCES 691

[269] P. Chavel and S. Lowenthal. Noise and coherence in optical image processing. II. Noisefluctuations. Journal of the Optical Society America, Vol. 68, pp. 721–732, 1978.

[270] Charng-Kann Chen and Ju-Hong Lee. McClellan transform based design techniques fortwo-dimensional linear-phase FIR filters. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications, Vol. 41(8), pp. 505–517, 1994.

[271] D. Chen, L.G. Durand and Z. Guo. Time-frequency analysis of the first heart sound. Part 2:An appropriate time-frequency representation technique. Medical & Biological Engineering &Computing. Vol. 35(4), pp. 311–317, 1997.

[272] D. Chen, L.G. Durand et al. Time-frequency analysis of the first heart sound: Part 3:Applicationto dogs with varying cardiac contractility and to patients with mitral mechanical prosthetic heartvalves. Medical & Biological Engineering & Computing. Vol. 35(5), pp. 455–461, 1997.

[273] D. Chen, L.G. Durand et al. Time-frequency analysis of the muscle sound of the humandiaphragm. Medical & Biological Engineering & Computing. Vol. 35(6), pp. 649–652, 1997.

[274] D.S. Chen and J.P. Allebach. Analysis of error in reconstruction of two-dimensional signalsfrom irregularly spaced samples. IEEE Transactions Acoust., Speech, Signal Processing,Vol. ASSP-35, pp. 173–179, 1987.

[275] F.R. Chen, H. Ichnose and J.J. Kai et al. Extension of HRTEM resolution by semi-blinddeconvolution method and Gerchberg-Saxton algorithm: application to grain boundary andinterface. Journal of Electron Microscopy, Vol. 50(6), pp. 529–540, 2001.

[276] G.X. Chen and Z.R. Zhou. Time-frequency analysis of friction-induced vibration underreciprocating sliding conditions. Digital signal processing. Vol. 17(1), pp. 371–393, 2007.

[277] Hong Chen and G.E. Ford.Aunified eigenfilter approach to the design of two-dimensional zero-phase FIR filters with the McClellan transform. IEEE Transactions on Circuits and Systems II:Analog and Digital Signal Processing, Vol. 43(8), pp. 622–626, 1996.

[278] K.H. Chen and C.C. Yang. On n-dimensional sampling theorems. Applied Math. Comput.,Vol. 7, pp. 247–252, 1980.

[279] W. Chen and S. Itoh. A sampling theorem for shift-invariant subspace. IEEE Transactions onSignal Processing, Vol. 46(10), pp. 2822–2824, 1998.

[280] D.K. Cheng and D.L. Johnson. Walsh transform of sampled time functions and the samplingprinciple. Proceedings IEEE, Vol. 61, pp. 674–675, 1973.

[281] Jingdong Chen, Bo Xu, and Taiyi Huang. New features based on the Cohen’s class of bilineartime-frequency representations for speech recognition. Proceedings 1998 Fourth InternationalConference on Signal Processing, 1998. ICSP ’98. Vol. 1, pp. 674–677, 1998.

[282] Victor C. Chen and Hao Ling. Time-Frequency Transforms for Radar Imaging and SignalAnalysis. Artech House Publishers, 2002.

[283] K.F. Cheung. The Generalized Sampling Expansion – Its Stability, Posedness and DiscreteEquivalent. M.S. thesis, Dept. Electrical Engr., Univ. of Washington, Seattle, Washington, 1983.

[284] K.F. Cheung. Image Sampling Density Reduction Below That of Nyquist. Ph.D. thesis,University of Washington, Seattle, 1988.

[285] K.F. Cheung and R.J. Marks II. Ill-posed sampling theorems. IEEE Transactions on Circuitsand Systems, Vol. CAS-32, pp. 829–835, 1985.

[286] K.F. Cheung, R.J. Marks II, and L.E.Atlas. Neural net associative memories based on convex setprojections, IEEE Proceedings 1st International Conference on Neural Networks, San Diego,June 1987.

[287] K.F. Cheung and R.J. Marks II. Papoulis’ generalization of the sampling theorem in higherdimensions and its application to sample density reduction. In Proceedings of the InternationalConference on Circuits and Systems, Nanjing, China, 1989.

[288] K.F. Cheung and R.J. Marks II. Image sampling below the Nyquist density without aliasing.Journal of the Optical Society America A, Vol. 7, pp. 92–105, 1990.

[289] K.F. Cheung, R.J. Marks II, and L.E. Atlas. Convergence of Howard’s minimum-negativity-constraint extrapolation algorithm. Journal of the Optical Society America A, Vol. 5,pp. 2008–2009, 1988.

[290] R. Cheung and Y. Rahmat-Samii. Experimental verification of nonuniform sampling techniquefor antenna far-field construction. Electromagnetics, Vol. 6, No. 4, pp. 277–300, 1986.


692 REFERENCES

[291] Francois Le Chevalier. Principles of Radar and Sonar Signal Processing. Artech HousePublishers, 2002.

[292] T.A.C.M. Claasen and W.F.G. Mecklenbrauker. The Wigner distribution, a tool for time-frequency signal analysis, Part 2: discrete time signals. Philips J. Res., Vol. 35, pp. 277–300,1980.

[293] T.A.C.M. Claasen and W.F.G. Mecklenbrauker. The Wigner distribution, a tool for time-frequency signal analysis, Part 3: relations with other time-frequency signal transformations.Philips J. Res., Vol. 35, pp. 373–389, 1980.

[294] D.G. Childers. Study and experimental investigation on sampling rate and aliasing in time-division telemetry systems. IRE Transactions Space Electronics & and Telemetry, pp. 267–283,1962.

[295] H.K. Ching. Truncation Effects in the Estimation of Two–Dimensional Continuous BandlimitedSignals. M.S. thesis, Dept. Electrical Engineering, Univ. of Washington, Seattle, 1985.

[296] P.C. Ching and S.Q. Wu. On approximated sampling theorem and wavelet denoising forarbitrary waveform restoration. IEEE Transactions on Circuits and Systems II - Analog andDigital Signal Processing, Vol. 45(8), pp. 1102–1106, 1998.

[297] P.S. Cho, H.G. Kuterdem, and R.J. Marks II, “A spherical dose model for radiosurgery planoptimization”, Phys. Med. Biol, Vol. 43, pp. 3145–3148, 1998.

[298] P.S. Cho, Shinhak Lee, R.J. Marks II, Seho Oh, S.G. Sutlief, and M.H. Phillips. Optimizationof intensity modulated beams with volume constraints using two methods: cost functionminimization and projections onto convex sets. Medical Physics. Vol. 25(4), pp. 435–443, 1998.

[299] H.I. Choi and W.J. Williams. Improved time-frequency representation of multi-componentsignals using exponential kernels. IEEE Transactions Acoust., Speech, and Sig. Proceedings,Vol. 37, pp. 862–871, 1989.

[300] Li Chongrong and Li Yanda. Recovery of acoustic impedance by POCS technique. 1991International Conference on Circuits and Systems, 1991. Conference Proceedings, China.,Vol. 2, pp. 820–823, 1991.

[301] J.J. Chou and L.A. Piegl. Data reduction using cubic rational B-splines. IEEE ComputerGraphics and Applications Magazine, Vol. 12(3), pp. 60–68, 1992.

[302] J. Chung, S.Y. Chung, and D. Kim. Sampling theorem for entire functions of exponentialgrowth. Journal of Mathematical Analysis and Applications, Vol. 265(1), pp. 217–228, 2002.

[303] Ruel V. Churchill. Fourier Series and Boundary Value Problems. McGraw-Hill. 2Rev Ededition, 1963.

[304] Ruel V. Churchill. Operational Mathematics. McGraw–Hill, New York, 1972.[305] T.A.C.M. Claasen and W.F.G. Mecklenbräuker. The Wigner distribution - a tool for time-

frequency signal analysis. Part I: Continuous-time signals; Part II: Discrete-time signals;Part III: Relations with other time-frequency signal transformations. Philips J. Res., Vol. 35,pp. 217–250, 276–300, 372–389, 1980.

[306] J.J. Clark. Sampling and reconstruction of non-bandlimited signals. In Proceedings VisualCommunication and Image Processing IV, SPIE, Vol. 1199, pp. 1556–1562, 1989.

[307] J.J. Clark, M.R. Palmer, and P.D. Lawrence. A transformation method for the reconstructionof functions from nonuniformly spaced samples. IEEE Transactions Acoust., Speech, SignalProcessing, Vol. ASSP-33, 1985.

[308] D. Cochran and J. Clark. On the sampling and reconstruction of time-warped bandlimitedsignals. Proceedings IASSP, pp. 1539–1541, 1990.

[309] L. Cohen. Generalized phase-space distribution functions. Journal Math. Phys., Vol. 7,pp. 781–786, 1966.

[310] L. Cohen. Time-frequency distributions - A review. Proceedings IEEE, Vol. 77, pp. 941–961,1989.

[311] D.D. Colclough and E.L. Titlebaum. Delay-Doppler POCS for specular multipath. ProceedingsIEEE International Conference on Acoustics, Speech, and Signal Processing, 2000, Vol. 4,pp. IV-3940–IV-3943, 2002.

[312] L. Cohen. Time Frequency Analysis: Theory and Applications. Prentice-Hall SignalProcessing, 1994.


REFERENCES 693

[313] T.W. Cole. Reconstruction of the image of a confined source. Astronomy and Astrophysics,pp. 41–45, 1973.

[314] T.W. Cole. Quasi-optical techniques in radio astronomy, In Progress in Optics, North-Holland,Amsterdam, 1977, pp. 187–244.

[315] Samuel Taylor Coleridge and Barbara E. Rooke. The Collected Works of Samuel TaylorColeridge, Volume 4: “The Friend” by Samuel Taylor Coleridge and Barbara E. Rooke.Princeton University Press, 1969.

[316] P.M. Colman. Non-Crystallographic symmetry and Sampling Theory. Zeitschrift furKristallographie, Vol. 140(5–6), pp. 344–349, 1974.

[317] R.J. Collier, C.B. Burckhardt, and L.H. Lin. Optical Holography. Academic Press,Orlando, FL., 1971.

[318] J.M. Combes, A. Grossman, and Ph. Tchamitchian, Wavelets, Springer-Verlag, 1989.[319] P.L. Combettes. The foundation of set theoretic estimation. Proceedings of the IEEE, Vol. 81,

pp. 182–208, 1993.[320] P.L. Combettes. Signal recovery by best feasible approximation. IEEE Transactions on Image

Processing, Vol. 2(2), pp. 269–271, 1993.[321] P.L. Combettes. Convex set theoretic image recovery by extrapolated iterations of parallel

subgradient projections. IEEE Transactions on Image Processing, Vol. 6(4), pp. 493–506,1997.

[322] J.W. Cooley and J.W. Tukey. An algorithm for the machine calculation of complex Fourierseries. Mathematics of Computation, Vol. 19(90), pp. 297–301, 1965.

[323] J.W. Cooley, P.A.W. Lewis, and P.D. Welch. Historical notes on the fast Fourier transform.IEEE Transactions on Audio Electroacoustics, Vol. AU-15(2), pp. 76–79, 1967.

[324] A. Consortini and F. Crochetti. An attempt to remove noise from histograms of probabilitydensity of irradiance in atmospheric scintillation. Proceedings SPIE, pp. 524–525, 1990.

[325] J.W. Cooley, P.A.W. Lewis, and P.D. Welch. The finite Fourier transform. IEEE TransactionsAudio Electroacoustics, Vol. AE-17, pp. 77–85, 1969.

[326] J.W. Cooley and J.W. Tukey. An algorithm for the machine calculations of complex Fourierseries. Math. Comput., Vol. 19, pp. 297–301, 1965.

[327] W.A. Coppel. et al. Fourier - on the occasion of his two hundredth birthday. Amer. Math.Monthly, Vol. 76, pp. 468–483, 1969.

[328] Joshua Corey. Fourier Series. Spineless Books, 2005.[329] I.J. Cox, C.J.R. Sheppard, and T. Wilson. Reappraisal of arrays of concentric annuli as super-

resolving filters. Journal of the Optical Society America, Vol. 72, pp. 1287–1291, 1982.[330] Edward J. Craig. Laplace and Fourier Transforms for Electrical Engineers. Holt, Rinehart

and Winston, 1964.[331] William Lane Craig. Time and Eternity: Exploring God’s Relationship to Time. Crossway

Books, 2001.[332] P.W. Cramer and W.A. Imbriale. Speed-up of near-field physical optics scattering calculations

by use of the sampling theorem. IEEE Transactions on Magnetics, Vol. 30(5), Part 2,pp. 3156–3159, 1994.

[333] R.E. Crochiere and L.R. Rabiner. Interpolation and decimation of digital signals – a tutorialreview. Proceedings IEEE, Vol. 69, pp. 300–331, 1981.

[334] R.E. Crochiere and L.R. Rabiner. Multirate Digital Signal Processing. Prentice-Hall,Englewood Cliffs, NJ, 1983.

[335] H.Z. Cummins and E.R. Pike, editors. Photon Correlation Spectroscopy and Velocimetry.Plenum Press, New York, 1977.

[336] L.J. Cutrona, E.N. Leith, C.J. Palermo, and L.J. Porcello. Optical data processing and filteringsystems. IRE Transactions Information Theory, pp. 386–400, 1960.

[337] B.S. Cybakov and V.P. Jakovlev. On the accuracy of restoring a function with a finite numberof terms of a Kotelnikov series. Radio Engineering & Electron., Vol. 4, pp. 274–275, 1959.

[338] R.N. Czerwinski and D.L. Jones. An adaptive time-frequency representation using a cone-shaped kernel. 1993 IEEE International Conference on Acoustics, Speech, and SignalProcessing, 1993. ICASSP-93., Vol. 4, pp. 404–407 1993.


694 REFERENCES

[339] R.N. Czerwinski and D.L. Jones. Adaptive cone-kernel time-frequency analysis. IEEETransactions on Signal Processing, Vol. 43(7), pp. 1715–1719, 1995.

D[340] J.J. DaCunha. Stability for time varying linear dynamic systems on time scales. Journal of

Computational and Applied Mathematics, Vol. 176(2), pp. 381–410, 2005.[341] J.J. DaCunha. Instability results for slowly time varying linear dynamic systems on time scales.

Journal of Mathematical Analysis and Applications, Vol. 328(2), pp. 1278–1289, 2007.[342] M.I. Dadi and R.J. Marks II. Detector relative efficiencies in the presence of Laplace noise.

IEEE Transactions on Aerospace and Electronic Systesm, Vol. AES-23(4), 1987.[343] W. Dahmen and C.A. Micchelli. Translates of multivariate splines. Linear Algebra Applications,

Vol. 52/53, pp. 217–234, 1983.[344] H. Dammann and K. Görtker. High-efficiency in-line multiple imaging by means of multiple

and filtering systems. Optical Communication, pp. 312–315, 1971.[345] R. Dandliker, E. Marom, and F.M. Mottier. Wavefront sampling in holographic interferometry.

Optical Communication, pp. 368–371, 1972.[346] H. D’Angelo. Linear Time Varying Systems, Analysis and Synthesis. Allyn and Bacon,

Boston, 1970.[347] I. Daubechies. The wavelet transform, time-frequency localization and signal analysis. IEEE

Transactions Inform. Theory IT-36, pp. 961–1005, 1990.[348] Joseph W. Dauben. Georg Cantor and Pope Leo XIII: Mathematics, Theology, and the Infinite.

Journal of the History of Ideas, Vol. 38(1), pp. 85–108, 1977.[349] Q.I. Daudpota, G. Dowrick, and C.A. Grwated. Estimation of moments of a Poisson sampled

random process. Journal Phys. A: Math. Gen., Vol. 10, pp. 471–483, 1977.[350] A.M. Davis. Almost periodic extension of bandlimited functions and its application to

nonuniform sampling. IEEE Transactions Circuits & Systems, Vol. CAS-33(10), pp. 933–938,1986.

[351] J.A. Davis, E.A. Merrill, D.M. Cottrell, and R.M. Bunch. Effects of sampling and binarizationin the output of the joint Fourier transform correlator. Optical Engineering, Vol. 29(9),pp. 1094–1100, 1990.

[352] John M. Davis, Ian A. Gravagne, Billy J. Jackson, Robert J. Marks II, and Alice A. Ramos. TheLaplace transform on time scales revisited. Journal of Mathematical Analysis Applications,Vol. 332, pp. 1291–1307, 2007.

[353] P.J. Davis. Interpolation and Approximation. Blaisdell, New York, 1963.[354] P. Davis and R. Hersh. The Mathematical Experience, Boston: Birkhäuser, 1981.[355] Sumner P. Davis, Mark C. Abrams, and James W. Brault. Fourier Transform Spectrometry.

Academic Press, 2001.[356] C. de Boor. On calculating with B–splines. Journal Approx. Theory, Vol. 6, pp. 50–62, 1972.[357] C. de Boor. A Practical Guide to Splines. Springer-Verlag, New York, 1978.[358] L.S. DeBrunner, V. DeBrunner, and Yao Minghua Yao. Edge-retaining asymptotic projections

onto convex sets for image interpolation. Proceedings of the 4th IEEE Southwest SymposiumImage Analysis and Interpretation, 2000. pp. 78–82, 2000.

[359] G. Defrancis. Directivity, super-gain and information. IRE Transactions Antennas &Propagation, Vol. AP-4, pp. 473–478, 1956.

[360] P. Delsarte and Y. Gemin. The split Levinson algorithm. IEEE Transactions Acoust., Speech,Signal Processing, Vol. ASSP-34, pp. 470–478, 1986.

[361] P. Delsarte and Y. Genin. On the role of orthogonal polynomials on the unit circle in digitalsignal processing applications. In Orthogonal Polynomials: Theory and Practice (ed. byP. Nevai and E. H. Ismail), Kluwer Academic Publishers, Dordrecht, pp. 115–133, 1990.

[362] Juan Arias de Reyna. Pointwise Convergence of Fourier Series. Springer, 2002.[363] Michael B. Marcus and Gilles Pisier. Random Fourier Series withApplications to Harmonic

Analysis. Annals of Mathematics Studies, Princeton University Press, 1981.[364] A. Desabata. Extension of a Finite Version of the Sampling Theorem. IEEE Transactions on

Circuits and Systems II- Analog and Digital Signal Processing, Vol. 41(12), pp. 821–823, 1994.


REFERENCES 695

[365] Rene Descartes, Discours de la Methode. 1637.[366] P. DeSantis, G. Guattari, F. Gori, and C. Palma. Optical systems with feedback. Opt. Acta,

pp. 505–518, 1976.[367] P. DeSantis and F. Gori. On an iterative method for super-resolution. Opt. Acta, pp. 691–695,

1975.[368] P. DeSantis, F. Gori, G. Guattari, and C. Palma. Emulation of super-resolving pupils through

image postprocessing. Optical Communication, pp. 13–16, 1986.[369] P. DeSantis, F. Gori, G. Guattari, and C. Palma. Synthesis of partially coherent fields. Journal

of the Optical Society America, Vol. 76, pp. 1258–1262, 1986.[370] P. DeSantis and C. Palma. Degrees of freedom of aberrated images. Opt. Acta, pp. 743–752,

1976.[371] A.J. Devaney and R. Chidlaw. On the uniqueness question in the problem of phase retrieval

from intensity measurements. Opt. Acta, pp. 1352–1354, 1978.[372] P. DeVincenti, G. Doro, and A. Saitto. Reconstruction of bi-dimensional electromagnetic field

by uni-dimensional sampling technique. Electron. Letters, Vol. 17, pp. 324–325, 1981.[373] G.M. Dillard. Method and apparatus for computing the discrete Fourier transform recursively.

United States Patent #4,023,028, 1977.[374] G.M. Dillard. Recursive computation of the DFT with applications to a pulse-doppler radar

system. Comput. and Elec. Engng., Vol. 1(1), pp. 143–152, 1973.[375] G.M. Dillard. Recursive computation of the discrete Fourier transform with applications to

an FSK communications receiver. IEEE National Telecommunication Conference, San Diego,pp. 263–265, 1974.

[376] Paul Adrien Maurice Dirac, Scientific American, 1963.[377] V.A. Ditkin and A.P. Prudnikiv. Integral Transforms and Operation Calculus, Fitmatgiz,

Moscow, 1961: English translation, Pergamon Press, New York, 1965.[378] D.D. Do and R.H. Weiland. Self–poissoning of catalyst pellets. AICHE Symp. Series, Vol.

77(202), pp. 36–45, 1981.[379] M.M. Dodson and A.M. Silva. Fourier analysis and the sampling theorem. Proceedings Royal

Irish Academy, Vol. 85 A, pp. 81–108, 1985.[380] A.H. Dooley. A non-abelian version of the shannon sampling theorem. SIAM Journal on

Mathematical Analysis, Vol. 20(3), pp. 624–633, 1989.[381] R.C. Dorf, M.C. Farren, and C.A. Philips. Adaptive sampling frequency for sampled data

control systems. IRE Transactions Automatic Control, Vol. AC-7, pp. 38–47, 1962.[382] C.N. dos Santos, S.L. Netto, L.W.R. Biscainho, and D.B. Graziosi. A modified constant-Q

transform for audio signals. Proceedings IEEE International Conference on Acoustics, Speech,and Signal Processing, 2004. (ICASSP ’04). Vol. 2, pp. 469–472, 2004.

[383] F. Dowla and J.H. McClellan. MEM spectral analysis for nonuniformly sampled signals. InProceedings of the 2nd International Conference on Computer Aided Seismic Analysis andDiscrimination, North Dartmouth, Mass., 1981.

[384] James F. Doyle. Wave Propagation in Structures: Spectral Analysis Using Fast DiscreteFourier Transforms. Springer, 2nd edition, 1997.

[385] E. Dubois. The sampling and reconstruction of time-varying imagery with application in videosystems. Proceedings IEEE, Vol. 23, pp. 502–522, 1985.

[386] Javier Duoandikoetxea and David Cruz-Uribe. Fourier Analysis. American MathematicalSociety, 2000.

[387] D.E. Dudgeon and R.M. Mersereau. Multidimensional Digital Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, 1984.

[388] P.M. Duffieux. L’integral de Fourier et ses applications a l’optique. Rennes-Oberthur, 1946.[389] R.J. Duffin and A.C. Schaeffer. Some properties of functions of exponential type. Bull. Amer.

Math. Society, Vol. 44, pp. 236–240, 1938.[390] R.J. Duffin and A.C. Schaeffer. A class of nonharmonic Fourier series. Transactions America

Math. Society, pp. 341–366, 1952.[391] J. Dunlop and V.J. Phillips. Signal recovery from repetitive non-uniform sampling patterns.

The Radio and Electronic Engineer, Vol. 44, pp. 491–503, 1974.


696 REFERENCES

[392] Chen Danmin, L.G. Durand, and H.C. Lee. Application of the cone-kernel distribution tostudy the effect of myocardial contractility in the genesis of the first heart sound in dog. 17thAnnual IEEE Conference on Engineering in Medicine and Biology Society, 1995. IEEE Vol. 2,pp. 959–960, 1995.

[393] K. Dutta and J.W. Goodman. Reconstruction of images of partially coherent objects fromsamples of mutual intensity. Journal of the Optical Society America, Vol. 67, pp. 796–803, 1977.

[394] J. Duvernoy. Estimation du nombre d’echantillons et du domaine spectral necessaires pourdeterminer une forme moyenne par une technique de superposition. Optical Communication,pp. 286–288, 1973.

[395] H. Dym and H.P. McKean. Fourier series and Integrals. Academic Press, New York, 1972.[396] H. Dym and H.P. McKean. Gaussian Processes, Function Theory, and the Inverse Spectral

Problem. Academic Press, New York, 1976.

E[397] Sir Arthur Eddington. The Philosophy of Physical Science. Cambridge, 1939.[398] R.E. Edwards. Fourier Series, a Modern Introduction. Springer; 2d ed edition, 1979.[399] M. Elad and A. Feuer. Restoration of a single superresolution image from several blurred,

noisy, and undersampled measured images. IEEE Transactions on Image Processing, Vol. 6(12),pp. 1646–1658, 1997.

[400] Tryon Edwards, The New Dictionary of Thoughts-A Cyclopedia of Quotations (Garden City,NY: Hanover House, 1852; revised and enlarged by C.H. Catrevas, Ralph Emerson Browns, andJonathan Edwards [descendent, along with Tryon, of Jonathan Edwards (1703–1758), presidentof Princeton], 1891.

[401] R.E. Edwards. Fourier Series, A Modern Introduction, Vol. 1. Holt, Rinehart and Winston,New York, 1967.

[402] Ethel Edwards. Carver of Tuskegee. (Cincinnati, Ohio; Ethyl Edwards & James T. Hardwick,1971) pp. 141–42.

[402a] A. Einstein, J. Mayer, and J. Holmes. Bite-Size Einstein: Quotations on Just About Everythingfrom the Greatest Mind of the Twentieth Century, St. Martin’s Press, 1996.

[403] P. Elleaume. Device for calculating a discrete moving window transform and application thereofto a radar system. United States Patent #4,723,125, 1988.

[404] P. Elleaume. Device for calculating a discrete Fourier transform and its application to pulsecompression in a radar system. United States Patent #4,772,889, 1988.

[405] M.K. Emresoy and P.J. Loughlin. Weighted least-squares implementation of Cohen-Posch timefrequency distributions with specified conditional and joint moment constraints.Proceedingsof the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis,pp. 305–308, 1998.

[406] M.K. Emresoy and P.J. Loughlin. Weighted least squares implementation of Cohen-Posch time-frequency distributions. IEEE Transactions on Signal Processing, Vol. 46(3), pp. 753–757,1998.

[407] M.K. Emresoy and P.J. Loughlin. Weighted least-squares implementation of Cohen-Poschtime-frequency distributions with specified conditional and joint moment constraints. IEEETransactions on Signal Processing, Vol. 47(3), pp. 893–900, 1999.

[408] A.G. Emslie and G.W. King. Spectroscopy from the point of view of the communicationtheory, II. Journal of the Optical Society America, Vol. 43, pp. 658–663, 1953.

[409] W. Engels and W. Splettstößer. A note on Maqusi’s proofs and truncation error bounds inthe dyadic (Walsh) sampling theorem. IEEE Transactions Acoust, Speech, Signal Processing,Vol. ASSP-30, pp. 334–335, 1982.

[410] W. Engels, E.L. Stark, and L. Vogt. Optimal kernels for a sampling theorem. Journal ofApproximate Theory, Vol. 50(1), pp. 69–83, 1987.

[411] W. Engels, E.L. Stark, and L. Vogt. On the application of an optimal spline sampling theorem.Signal Processing, Vol. 14(3), pp. 225–236, 1988.

[412] A. Ephremides and L.H. Brandenburg. On the reconstruction error of sampled data estimates.IEEE Transactions Information Theory, Vol. IT-19, pp. 365–367, 1973.


REFERENCES 697

[413] A. Erdelyi et al. Higher Transcendental Functions, Vol. 1. McGraw-Hill, New York, 1953.[414] A. Erdelyi et al. Tables of Integral Transforms II. McGraw-Hill, New York, 1954.[415] M.F. Erden, M.A. Kutay, and H.M. Ozaktas. Repeated filtering in consecutive fractional Fourier

domains and its application to signal restoration. IEEE Transactions on Signal Processing,Vol. 47(5), pp. 1458–1462, 1999.

[416] T. Ericson. A generalized version of the sampling theorem. Proceedings IEEE, Vol. 60,pp. 1554–1555, 1972.

[417] P.E. Eren, M.I. Sezan, and A.M. Tekalp. Robust, object-based high-resolution imagereconstruction from low-resolution video. IEEE Transactions on Image Processing, Vol. 6(10),pp. 1446–1451, 1997.

[418] T. Erseghe, P. Kraniauskas, G. Cariolaro. Unified fractional Fourier transform and samplingtheorem. IEEE Transactions on Signal Processing, Vol. 47(12), pp. 3419–3423, 1999.

[419] Okan K. Ersoy. Diffraction, Fourier Optics and Imaging. Wiley-Interscience, 2006.[420] A. Erteza and K.S. Lin. On the transform property of a bandlimited function and its samples.

Proceedings IEEE, Vol. 68, pp. 1149–1150, 1980.[421] G. Bora Esmer, Vladislav Uzunov, Levent Onural, Haldun M. Ozaktas, and Atanas Gotchev.

Diffraction field computation from arbitrarily distributed data points in space. SignalProcessing – Image Communication. Vol. 22(2), pp. 178–187, 2007.

[422] H. Eves. Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.[423] H. Eves. Mathematical Circles Adieu, Boston: Prindle, Weber and Schmidt, 1977.[424] H. Eves. Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.

F[425] G.S. Fang. Whittaker-Kotelnikov-Shannon sampling theorem and aliasing error. Journal of

Approximation Theory, Vol. 85(2), pp. 115–131, 1996.[426] W.H. Fang, H.S. Hung, C.S. Lu, and P.C. Chu. Block adaptive beamforming via parallel pro-

jection method. IEICE Transactions on Communications, Vol. E88B(3), pp. 1227–1233, 2005.[427] N.H. Farhat and G.P. Shah. Implicit sampling in optical data processing. Proceedings SPIE,

Vol. 201, pp. 100–106, 1979.[428] A. Faridani. A generalized sampling theorem for locally compact abelian groups. Mathematics

of Computation, Vol. 63(207), pp. 307–327, 1994.[429] Thomas C. Farrar and Edwin D. Becker. Pulse and Fourier Transform NMR: Introduction

to Theory and Methods. Academic Press, 1971.[430] H.G. Feichtinger. Wiener amalgam spaces and some of their applications. In Conf. Proceedings

Function spaces, Edwardsville, IL., Marcel Dekker, New York, April 1990.[431] E.B. Felstead and A.U. Tenne-Sens. Optical interpolation with application to array processing.

Applied Optics, Vol. 14, pp. 363–368, 1975.[432] M.M. Fenoy and P. Ibarrola. The optional sampling theorem for submartingales in the

sequentially planned context. Statistics and Probability Letters, Vol. 77(8), pp. 826–831, 2007.[433] W.L. Ferrar. On the cardinal function of interpolation–theory. Proceedings Royal Society

Edinburgh, Vol. 45, pp. 267–282, 1925.[434] W.L. Ferrar. On the cardinal function of interpolation–theory. Proceedings Royal Society

Edinburgh, Vol. 46, pp. 323–333, 1926.[435] W.L. Ferrar. On the consistency of cardinal function interpolation. Proceedings Royal Society

Edinburgh, Vol. 47,pp. 230–242, 1927.[436] Thomas Clark Farrar and Edwin D. Becker. Pulse and Fourier Transform NMR:

Introduction to Theory and Methods. Elsevier Science & Technology, 1971.[437] John R. Ferraro, Louis J. Basile. Fourier Transform Infrared Spectroscopy, Academic Press,

1985.[438] John R. Ferraro, Louis J. Basile (Editors). Fourier Transform Infrared Spectra:Applications

to Chemical Systems, Vol. 1. Elsevier Science & Technology Books, 1978.[439] Paulo J.S.G. Ferreira. Incomplete sampling series and the recovery of missing samples

from oversampled band-limited signals. IEEE Transactions Signal Processing, Vol. 40, 1992.pp. 225–227.


698 REFERENCES

[440] Paulo J.S.G. Ferreira. Interpolation and the discrete Papoulis-Gerchberg algorithm. IEEETransactions on Signal Processing, Vol. 42(10), pp. 2596–2606, 1994.

[441] H.A. Ferweda. The phase reconstruction problem for wave amplitudes and coherence functions.In Inverse Source Problems in Optics, H.P. Baltes, editor, Springer-Verlag, Berlin, 1978.

[442] H.A. Ferweda and B.J. Hoenders. On the reconstruction of a weak phase-amplitude object IV.Optik, pp. 317–326, 1974.

[443] Alfred Fettweis, Josef A. Nossek, and Klaus Meerkötter. Reconstruction of signals afterfiltering and sampling rate reduction. IEEE Transactions Acoust., Speech, Signal Processing,Vol. ASSP-33, No. 4, pp. 893–902, 1985.

[444] M.A. Fiddy and T.J. Hall. Nonuniqueness of super-resolution techniques applied to sampleddata. Journal of the Optical Society America, Vol. 71, pp. 1406–1407, 1981.

[445] G. Fielding, R. Hsu, P. Jones, et al. Aliasing and reconstruction distortion in digitalintermediates. SMPTE Motion Imaging Journal, Vol. 115(4), pp. 128–136, 2006.

[446] A.R. Figueiras-Vidal, J.B. Marino-Acebal, and R.G. Gomez. On generalized samplingexpansions for deterministic signals. IEEE Transactions Circuits & Systems, Vol. CAS-28,pp. 153–154, 1981.

[447] G. Fix and G. Strang. Fourier analysis of the finite element method in Ritz-Galerkin theory.Studies Applied Math. Vol. 48, pp. 268–273, 1969.

[448] I.T. Fjallbrandt. Method of data reduction of sampled speech signals by using nonuniformsampling and a time variable digital filter. Electron. Letters, Vol. 13, pp. 334–335, 1977.

[449] T.T. Fjallbrandt. Interpolation and extrapolation in nonuniform sampling sequences withaverage sampling rate below the Nyquist rate. Electron. Letters, Vol. 11, pp. 264–266, 1975.

[450] G.C. Fletcher and D.J. Ramsay. Photon correlation spectroscopy of polydisperse samples,I. Histogram method with exponential sampling. Opt. Acta, Vol. 30, pp. 1183–1196, 1983.

[451] N.J. Fliege. Multirate Digital Signal Processing: Multirate Systems - Filter Banks -Wavelets. Wiley, 2000.

[452] L. Fogel. A note on the sampling theorem. IRE Transactions, Vol. 1, pp. 47–48, 1955.[453] J.T. Foley, R.R. Butts. Sampling Theorem for the Reconstruction of Bandlimited Intensities

from Their Spatially Averaged Values. Journal of the Optical Society of America, Vol. 72(12),pp. 1812–1812, 1982.

[454] Gerald B. Folland. Fourier Analysis and Its Applications. Brooks Cole, 1992.[455] Joseph Fourier. The Analytical Theory of Heat. Cosimo Classics, 2007.[456] William T. Fox. FourierAnalysis of Weather and Wave Data from Lake Michigan. Williams

College, 1970.[457] J. Frank. Computer processing of electron micrographs. InAdvanced Techniques in Biological

Electron Microscopy, J.K. Koehler, editor, Springer-Verlag, New York, 1973.[458] G. Franklin. Linear filtering of sampled data. IRE International Conv. Rec., Vol. 3, Pt. 4,

pp. 119–128, 1955.[459] L.E. Franks. Signal Theory. Prentice-Hall, Englewood Cliffs, NJ, 1969.[460] D. Fraser. A Conceptual Image Intensity Surface and the Sampling Theorem. Australian

Computer Journal, Vol. 19(3), pp. 119–125, 1987.[461] H. Freeman. Discrete Time Systems. John Wiley, New York, 1965.[462] A.T. Friberg. On the existence of a radiance function for finite planar sources of arbitrary states

of coherence. Journal of the Optical Society America, Vol. 69, pp. 192–199, 1979.[463] B.R. Frieden. Image evaluation by the use of sampling theorem. Journal of the Optical Society

America, Vol. 56, pp. 1355–1362, 1966.[464] B.R. Frieden. On arbitrarily perfect imagery with a finite aperture. Opt. Acta, pp. 795–807, 1969.[465] B.R. Frieden. Evaluation, design and extrapolation methods for optical signals, based on the use

of the prolate functions. In Progress in Optics, E. Wolf, editor, North-Holland, Amsterdam, 1971.[466] B.R. Frieden. Image enhancement and restoration. In Picture processing and digital filtering,

Springer-Verlag, Berlin, 1975.[467] B.R. Frieden. Band-unlimited reconstruction of optical objects and spectra. Journal of the

Optical Society America, Vol. 66, pp. 1013–1019, 1976.[468] Michael Fripp, Deborah Fripp, and Jon Fripp. Speaking of Science. Newnes, 2000.


REFERENCES 699

[469] T. Fujita and M.R. McCartney. Phase recovery for electron holography using Gerchberg-Papoulis iterative algorithm. Ultramicroscopy, Vol. 102(4), pp. 279–286, 2005.

[470] Y.H. Fung, Y.H. Chan. POCS-based algorithm for restoring colour-quantised images. IEEProceedings Vision, Image and Signal Processing, Vol. 151(2), pp. 119–127, 2004.

[471] Y.H. Fung and Y.H. Chan. A POCS-based restoration algorithm for restoring halftoned color-quantized images. IEEE Transactions on Image Processing, Vol. 15(7), pp. 1985–1992, 2006.

G[472] N.T. Gaardner. Multidimensional Sampling Theorem. Proceedings of the IEEE, Vol. 60(2),

p. 247, 1972.[473] D. Gabioud. Effect of irregular sampling, especially in the case of justification jitter.

Mitteilungen AGEN, No. 44, pp. 39–46, 1986.[474] D. Gabor.Theory of communication. Journal IEE (London),Vol. 93, Part III, pp. 429–457, 1946.[475] D. Gabor. A new microscopic principle. Nature, pp. 777–779, 1948.[476] D. Gabor. Light and information. In Progress in Optics, E. Wolf, editor, North-Holland,

Amsterdam, 1961.[477] V. Galdi, V. Pierro and I.M. Pinto. Evaluation of Stochastic Resonance Based Detectors of

Weak Harmonic Signals in Additive White Gaussian Noise. Physical Review E, Vol. 55(6),p. 57, 1998.

[478] N.C. Gallagher, Jr., and G.L. Wise. A representation for band-limited functions. ProceedingsIEEE, Vol. 63, p. 1624, 1975.

[479] H. Gamo. Intensity matrix and degrees of coherence. Journal of the Optical Society America,Vol. 47, p. 976, 1957.

[480] H. Gamo. Transformation of intensity matrix by the transmission of a pupil. Journal of theOptical Society America, Vol. 48, pp. 136–137, 1958.

[481] H. Gamo. Matrix treatment of partial coherence. In Progress in Optics, E. Wolf, editor, North-Holland, Amsterdam, 1964.

[482] George Gamow. One two three … infinity: Facts and speculations of science. NewAmericanLibrary, Mentor book edition (1953). Reprinted by Dover Publications, 1988.

[483] M. Gamshadzahi. Bandwidth reduction in delta modulation systems using an iterativereconstruction scheme. Master’s thesis, Department of ECE, Illinois Institute of Technology,Chicago, December, 1989.

[484] X.C. Gan,A.W.C. Liew, and H.Yan. Microarray missing data imputation based on a set theoreticframework and biological knowledge. Nucleic Acids Research,Vol. 34(5), pp. 1608–1619, 2006.

[485] William L. Gans. The measurement and deconvolution of time jitter in equivalent-timewaveform samplers. IEEE Transactions Instrumentation & Measurement, Vol. IM-32(1),pp. 126–133, 1983.

[486] William L. Gans. Calibration and error analysis of a picosecond pulse waveform measurementsystem at NBS. Proceedings IEEE, Vol. 74, No. 1, pp. 86–90, 1986.

[487] A.G. Garcia, M.A. Hemandez-Medina. The discrete Kramer sampling theorem andindeterminate moment problems. Journal of Computational and Applied Mathematics,Vol. 134(1–2), pp. 13–22, 2001.

[488] Garcia F.M., I.M.G. Lourtie, and J. Buescu. L2 nonstationary processes and the samplingtheorem. IEEE Signal Processing Letters, Vol. 8(4), pp. 117–119, 2001.

[489] P.H. Gardenier, C.A. Lim, D.G.H. Tan et al. Aperture distribution phase from singleradiation-pattern measurement via Gerchberg-Saxton algorithm. Electronic Letters, Vol. 22(2),pp. 113–115, 1986.

[490] N.T. Garder. A note on multidimensional sampling theorem. Proceedings IEEE, Vol. 60,pp. 247–248, 1972.

[491] W.A. Gardner. A sampling theorem for nonstationary random processes. IEEE TransactionsInformation Theory, Vol. IT-18, pp. 808–809, 1972.

[492] H. Garudadri and E. Velez. A comparison of smoothing kernels for computing bilinear time-frequency representations. IEEE 1991 International Conference on Acoustics, Speech, andSignal Processing, 1991. ICASSP-91., Vol. 5., pp. 3221–3224, 1991.


700 REFERENCES

[493] J.D. Gaskill. Linear Systems, Fourier Transforms and Optics. John Wiley & Sons, Inc.,New York, 1978.

[494] M. Gaster and J.B. Roberts. Spectral analysis of randomly sampled signals. Journal InstituteMath. Applic., Vol. 15, pp. 195–216, 1975.

[495] G.C. Gaunaurd and H.C. Strifors. Signal analysis by means of time-frequency (Wigner-type)distributions-Applications to sonar and radar echoes. Proceedings of the IEEE. Vol. 84(9),pp. 1231–1248, 1996.

[496] W.S. Geisler and D.B. Hamilton. Sampling theory analysis of spatial vision. Journal of theOptical Society America A, Vol. 3, pp. 62–70, 1986.

[497] F.J. Geng, D.M. Zhu DM and Q.Y. Lu. A new existence result for impulsive dynamic equationson timescales. Applied Mathematics Letters, Vol. 20(2), pp. 206–212, 2007.

[498] T. Gerber and P.W. Schmidt. The sampling theorem and small-angle scattering. Journal AppliedCrystallography, Vol. 16, pp. 581–589, 1983.

[499] T. Gerber, G. Walter, and P.W. Schmidt. Use of the Sampling Theorem for CollimationCorrections in Small Angle X-Ray Scatteing. Journal of Applied Crystallography, Vol. 24,Part 4, pp. 278–285, 1991.

[500] R.W. Gerchberg. Super-resolution through error energy reduction. Optica Acta, Vol. 21,pp. 709–720, 1974.

[501] R.W. Gerchberg and W.O. Saxton. A practical algorithm for the determination of phase fromimage and diffraction plane pictures. Optik. 35, pp. 237–246, 1972.

[502] R.W. Gerchberg. The lock problem in the Gerchberg-Saxton algorithm for phase retrieval.Optik, Vol. 74(3), pp. 91–93, 1986.

[503] Allen Gersho. Asymptotically optimal block quantization. IEEE Transactions InformationTheory, Vol. IT-25, pp. 373–380, 1979.

[504] A. Gersho and R. Gray. Vector Quantization and Signal Compression. Kluwer AcademicPublishers, 1992.

[505] G. Gheen and F.T.S. Yu. Broadband image subtraction by spectral dependent sampling. OpticalCommunication, pp. 335–341, 1986.

[506] Charles R. Giardina and Edward R. Dougherty, Morphological Methods in Image and SignalProcessing, Prentice-Hall, 1988.

[507] R.J. Glauber. Coherent and incoherent states of the radiation field. Phys. Rev., pp. 2766–2788,1963.

[508] M.J.E. Golay. Point arrays having compact, nonredundant autocorrelations. Journal of theOptical Society America, Vol. 61, pp. 272–273, 1971.

[509] M.H. Goldburg and R.J. Marks II. Signal synthesis in the presence of an inconsistent set ofconstraints. IEEE Transactions Circuits & Systems, Vol. CAS-32, pp. 647–663, 1985.

[510] S. Goldman. Information Theory. Dover, New York, 1968.[511] Rafael C. Gonzalez. Digital Image Processing. Addison-Wesley Publishing Company, Inc.,

Reading, MA., 1977.[512] Enrique A. Gonzalez-Velasco. Fourier Analysis and Boundary Value Problems. Academic

Press, 1995.[513] I.J. Good. The loss of information due to clipping a waveform. Information & Control, Vol. 10,

pp. 220–222, 1967.[514] J.W. Goodman. Introduction to Fourier Optics. McGraw-Hill, New York, 1968. (A revised

version is also available [518].)[515] J.W. Goodman. Imaging with low-redundancy arrays, In Applications of holography, Plenum

Press, New York, pp. 49–55, 1971.[516] J.W. Goodman. Linear space-variant optical data processing. In Optical Information

Processing, S.H. Lee, editor, Springer-Verlag, New York, 1981.[517] J.W. Goodman. Statistical Optics. Wiley, New York, 1985.[518] J.W. Goodman. Introduction to Fourier Optics Third Edition, Roberts & Company

Publishers 2004. (This is a revised version of [514].)[519] G.C. Goodwin, M.B. Zarrop, and R.L. Payne. Coupled design of test signals, sampling intervals,

and filters for system identification. IEEE Transactions Automatic Control, Vol. AC-19, 1974.


REFERENCES 701

[520] R.A. Gopinath, J.E. Odegard and C.S. Burrus. Optimal Wavelet Representation of Signals andthe Wavelet Sampling Theorem. IEEE Transactions on Circuits and Systems II-Analog andDigital Signal Processing, Vol. 41(4), pp. 262–277, 1994.

[521] W.J. Gordon and R.F. Riesenfeld. B-spline curves and surfaces. In ComputerAided GeometricDesign, R. Barnbill and R.F. Riesenfeld, editors, Academic Press, New York, 1974.

[522] F. Gori. Integral equations for incoherent imagery. Journal of the Optical Society America,Vol. 64, pp. 1237–1243, 1974.

[523] F. Gori. On an iterative method for super-resolution. International Optics Computing Conf.,IEEE Catalog no. 75 CH0941-5C, pp. 137–141, 1975.

[524] F. Gori. Lau effect and coherence theory. Optical Communication, pp. 4–8, 1979.[525] F. Gori. Fresnel transform and sampling theorem. Optical Communication,Vol. 39, pp. 293–298,

1981.[526] F. Gori and R. Grella. The converging prolate spheroidal functions and their use in Fresnel

optics. Optical Communication, pp. 5–10, 1983.[527] F. Gori and G. Guattari. Effects of coherence on the degrees of freedom of an image. Journal

of the Optical Society America, Vol. 61, pp. 36–39, 1971.[528] F. Gori and G. Guattari. Holographic restoration of nonuniformly sampled bandlimited

functions. Optical Communication, Vol. 3, pp. 147–149, 1971.[529] F. Gori and G. Guattari. Imaging systems using linear arrays of non-equally spaced elements.

Phys. Letters, Vol 32A, pp. 38–39, 1970.[530] F. Gori and G. Guattari. Nonuniform sampling in optical processing. Optica Acta, Vol. 18,

pp. 903–911, 1971.[531] F. Gori and G. Guattari. Optical analog of a non-redundant array. Phys. Letters Vol. 32A,

pp. 446–447, 1970.[532] F. Gori and G. Guattari. Use of nonuniform sampling with a single correcting operation. Optical

Communication, Vol. 3, pp. 404–406, 1971.[533] F. Gori and G. Guattari. Shannon number and degrees of freedom of an image. Optical

Communication, pp. 163–165, 1973.[534] F. Gori and G. Guattari. Degrees of freedom of images from point-like element pupils. Journal

of the Optical Society America, Vol. 64, pp. 453–458, 1974.[535] F. Gori and G. Guattari. Eigenfunction technique for point-like element pupils. Opt. Acta,

pp. 93–101, 1975.[536] F. Gori and G. Guattari. Signal restoration for linear systems with weighted inputs;

singular value analysis for two cases of low-pass filtering. Inverse Problems, pp. 67–85,1985.

[537] F. Gori, G. Guattari, C. Palma, and M. Santarsiero. Superresolving postprocessing for incoherentimagery. Optical Communication, pp. 98–102, 1988.

[538] F. Gori and F. Mallamace. Interference between spatially separated holographic recordings.Optical Communication Vol. 8, pp. 351–354, 1973.

[539] F. Gori and C. Palma. On the eigenvalues of the sinc kernel. Journal Phys. A, Math. Gen.,pp. 1709–1719, 1975.

[540] F. Gori, S. Paolucci, and L. Ronchi. Degrees of freedom of an optical image in coherentillumination, in the presence of aberrations. Journal of the Optical Society America, Vol. 65,pp. 495–501, 1975.

[541] F. Gori and L. Ronchi. Degrees of freedom for scatterers with circular cross section. Journalof the Optical Society America, Vol. 71, pp. 250–258, 1981.

[542] F. Gori and S. Wabnitz. Modifications of the Gerchberg method applied to electromagneticimaging, In Inverse Methods in Electromagnetic Imaging, D. Reidel Publishing Co.,Dordrecht, 1985, pp. 1189–1203.

[543] D. Gottlieb and S.A. Orszag. Numerical Analysis of Spectral Methods-Theory andApplications. SIAM Publ., Philadelphia, 1977.

[544] I.S. Gradshteyn, I.M. Ryzhik, and Alan Jeffrey. Tables of Integrals, Products and Series, 5thEdition. Academic Press, New York, 1994.

[545] Loukas Grafakos. Classical and Modern Fourier Analysis. Prentice Hall, 2003.


702 REFERENCES

[546] I. Grattan-Guinness. Joseph Fourier and the revolution in mathematical physics. Journal of theInstitute of Mathematics and its Applications, Vol. 5, pp. 230–253, 1969.

[547] I. Grattan-Guinness. Joseph Fourier, 1768–1830. London, 1972.[548] Ian A. Gravagne, John M. Davis, Jeffrey J. DaCunha and R.J. Marks II. Bandwidth Reduction

for Controller Area Networks using Adaptive Sampling. Proc. Int. Conf. Robotics andAutomation (ICRA), New Orleans, LA, pp. 5250–5255, 2004.

[549] R.M. Gray, A. Buzo, A.H. Gray, Jr., and Y. Matsuyama. Distortion measures for speechprocessing. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-28, pp. 367–376,1980.

[550] P. Greguss and W. Waigelich. Ultrasonic Holographic Fourier Spectroscopy via Optical FourierTransforms. IEEE Transactions on Computers, Vol. C-24(4), pp. 412–418, 1975.

[551] U. Grenader and G. Szegö. Toeplitz Forms and theirApplications. University of CaliforniaPress, Berkeley, CA., 1958.

[552] M. Grigoriu. Simulation of Stationary Process via a Sampling Theorem. Journal of Sound andVibration, Vol. 166(2), pp. 301–313, 1993.

[553] B. Grobler. Practical application of the sampling theorem. Feingerätetechnik, Vol. 26,pp. 342–345, 1977.

[554] D. Groutage. The calculation of features for non-stationary signals from moments of the singularvalue decomposition of Cohen-Posch (positive time-frequency) distributions. Proceedingsof the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis,pp. 605–608, 1998.

[555] D. Groutage and D. Bennink. Feature sets for nonstationary signals derived from momentsof the singular value decomposition of Cohen-Posch (positive time-frequency) distributions.IEEE Transactions on Signal Processing, Vol. 48(5), pp. 1498–1503, 2000.

[556] B.Y. Gu, B.Z. Dong, and G.Z. Yang. A New Algorithm for Retrieval Phase Using the SamplingTheorem. Optik, Vol. 75(3), pp. 92–96, 1987.

[557] C.R. Guarino. A new method of spectral analysis and sample rate reduction for bandlimitedsignals. Proceedings IEEE, Vol. 69, pp. 61–63, 1981.

[558] L.G. Gubin, B.T. Polyak, and E.V. Ralik. The method of projections for finding the commonpoint of convex sets. USSR Comput. Math. Phys., Vol. 7(6), pp. 1–24, 1967.

[559] B.K. Gunturk, Y. Altunbasak and R.M. Mersereau. Color plane interpolation using alternatingprojections. IEEE Transactions on Image Processing. Vol. 11(9), pp. 997–1013, 2002.

[560] B.K. Gunturk, Y. Altunbasak and R.M. Mersereau. Multiframe resolution-enhancementmethods for compressed video. IEEE Signal Processing Letters, Vol. 9(6), pp. 170–174, 2002.

[561] S.C. Gupta. Increasing the sampling efficiency for a control system. IEEE TransactionsAutomatic Control, Vol. AC-8, pp. 263–264, 1963.

[562] R.K. Guy. Mersenne Primes, Repunits, Fermat Numbers, Primes of Shape k · 2n + 2 [sic],in Unsolved Problems in Number Theory, 2nd ed., New York: Springer-Verlag, pp. 8–13,1994.

H[563] M.K. Habib and S. Cambanis. Dyadic sampling approximations for non-sequency-limited

signals. Information & Control, Vol. 49, pp. 199–211, 1981.[564] M.K. Habib and S. Cambanis. Sampling approximation for non-bandlimited harmonizable

random signals. Inform. Sci., Vol. 23, pp. 143–152, 1981.[565] A.H. Haddad and J.B. Thomas. Integral representation for non-uniform sampling expansions.

In Proceedings 4th Allerton Conference of Circuit System Theory, pp. 322–333, 1966.[566] A.H. Haddad, K. Yao, and J.B. Thomas. General methods for the derivation of sampling

theorems. IEEE Transactions Information Theory, Vol. IT-13, 1967.[567] M.O. Hagler, R.J. Marks II, E.L. Kral, J.F. Walkup, and T.F. Krile. Scanning technique for

coherent processors. Applied Optics, Vol. 19, pp. 1670–1672, 1980.[568] H. Hahn. Über das Interpolation problem. Math. Z., Vol. 1, pp. 115–142, 1918.[569] E. Hansen. Fast Hankel transform algorithm. IEEE Transactions on Acoustics, Speech, and

Signal Processing. Vol. 33(3), pp. 666–671, 1985.


REFERENCES 703

[570] M.W. Hall and R.J. Marks II. Sampling Theorem Characterization of Variation LimitedSystems at Reduced Sampling Rates. Journal of the Optical Society of America, Vol. 68(10),pp. 1362–1362, 1978.

[571] J. Hamill, G.E. Caldwell and T.R. Derrick. Reconstructing digital signals using Shannon’sSampling Theorem. Journal of Applied Biomagnetics, Vol. 13(2), pp. 226–238, 1997.

[572] Richard W. Hamming. Numerical Methods for Scientists and Engineers. McGraw-Hill,New York, 1962.

[573] Richard W. Hamming. The Unreasonable Effectiveness of Mathematics. The AmericanMathematical Monthly, Vol. 87(2), 1980.

[574] Richard W. Hamming. Digital Filters: Third Edition, Dover Publications, 1998.[575] R.C. Hansen. Phased Array Antennas. Wiley-Interscience, 1998.[576] R.M. Haralick and L.G. Shapiro. Computer and Robot Vision. Addison-Wesley, 1991.[577] R.M. Haralick, X.H. Zhuang, C. Lin et al. The Digital Morphological Sampling Theorem. IEEE

Transactions on Acoustics, Speech and Signal Processing, Vol. 37(12), pp. 2067–2090, 1989.[578] Robert M. Haralick, Mathematical Morphology: Theory and Hardware (Oxford Series in

Optical and Imaging Sciences) 2005.[579] R.D. Harding. Fourier Series and Transforms. Taylor & Francis, 1985.[580] G.H. Hardy and W.W. Rogosinski. Fourier Series. Dover Publications, 1999.[581] J.L. Harris. Diffraction and resolving power. Journal of the Optical Society America, Vol. 54,

pp. 931–936, 1964.[582] C.J. Hartley. Resolution of frequency aliases in ultrasonic pulsed doppler velocimeters. IEEE

Transactions Sonics & Ultrasonics, Vol. SU-28, pp. 69–75, 1981.[583] R. Hartley and K. Welles II. Recursive computation of the Fourier transform. Proceedings of

the 1990 IEEE International Symposium on Circuits and Systems, pp. 1792–1795.[584] Joseph Havlicek. The Fourier Transform. Morgan & Claypool Publishers, 2007.[585] Stephen Hawking. A Brief History of Time. Bantam Books, 1996.[586] S. Haykin. Introduction to Adaptive Filters. MacMillan, New York, 1976.[587] M. Hedley, H. Yan, and D. Rosenfeld. A modified Gerchberg-Saxton algorithm for one-

dimensional motion artifact correction in MRI. IEEE Transactions on Signal Processing,Vol. 39, pp. 1428–1433, 1991.

[588] Z.S. Hegedus. Annular pupil arrays; application to confocal scanning. Opt. Acta, pp. 815–826,1985.

[589] S. Hein and A. Zakhor. Reconstruction of oversampled band-limited signals from σ� encodedbinary sequences IEEE Transactions on Signal Processing, Vol. 42(4), pp. 799–811, 1994.

[590] H.D. Helms and J.B. Thomas. Truncation error of sampling theorem expansion. ProceedingsIRE, Vol. 50, pp. 179–184, 1962.

[591] C.W. Helstrom. An expansion of a signal in Gaussian elementary signals. IEEE TransactionsInformation Theory, Vol. IT-12, pp. 81–82, 1966.

[592] S.S. Hemami et al. Engineering Transform coded image reconstruction exploiting interblockcorrelation. IEEE Transactions Image Processing, Vol. 4(7), pp. 1023–1027, 1995.

[593] J. Henderson and C.C. Tisdell. Topological transversality and boundary value problems ontime scales. Journal of Mathematical Analysis and Applications, Vol. 289(1), pp. 110–125,2004.

[594] J. Herivel. The influence of Fourier on British mathematics. Centaurus, Vol. 17(1), pp. 40–57,1972.

[595] John Herivel. Joseph Fourier: The Man and the Physicist. Oxford University Press, 1975.[596] G.T. Herman, ed., Image Reconstruction from Projections Springer-Verlag, Berlin, 1979.[597] G.T. Herman, J. Zheng, and C.A. Bucholtz. Shape-based interpolation. IEEE Computer

Graphics and Applications Magazine, Vol. 12, No. 3, pp. 69–79, May 1992.[598] A.O. Hero III and D. Blatt. Sensor network source localization via projection onto convex

sets (POCS). Proceedings IEEE International Conference on Acoustics, Speech, and SignalProcessing, Vol. 3, pp. iii/689–iii/692, 2005.

[599] R.S. Hershel, P.W. Scott, and T.E. Shrode. Image sampling using phase gratings. Journal of theOptical Society America, Vol. 66, pp. 861–863, 1976.


704 REFERENCES

[600] J.R. Higgins. An interpolation series associated with the Bessel-Hankel transform. JournalLondon Math. Society, Vol. 5, pp. 707–714, 1972.

[601] J.R. Higgins. A sampling theorem for irregularly spaced sample points. IEEE TransactionsInformation Theory, Vol. IT-22, pp. 621–622, 1976.

[602] J.R. Higgins. Completeness and Basis Properties of Sets of Special Functions. CambridgeUniversity Press, Cambridge, 1977.

[603] J.R. Higgins. Five short stories about the cardinal series. Bull. America Math. Society, Vol. 12,pp. 45–89, 1985.

[604] J.R. Higgins. Sampling theorems and the contour integral method. Applied Anal., Vol. 41,pp. 155–169, 1991.

[605] J.R. Higgins Sampling Theory in Fourier and Signal Analysis: Foundations. OxfordUniversity Press, 1996.

[606] J.R. Higgins and Rudolph L. Stens (Editors). Sampling Theory in Fourier and SignalAnalysis: Advanced Topics, Vol. 2, Oxford University Press, 1999.

[607] S. Hilger. Ein Maβkettenkalkulül mit Awendung auf Zentrumsmannigfaltigkeitem. Ph.D.thesus, Univerität Würzburg, 1988.

[608] S. Hilger. Special Functions: Laplace and Fourier Transform on Measure Chains. DynamicSystems and Applications, Vol. 8, pp. 471–488, 1999.

[609] S. Hilger. An Application of Calculus on Measure Chains to Fourier Theory and Heisenberg’sUncertainty Principle. Journal of Difference Equations and Applications, Vol. 8, pp. 897–936,2002.

[610] N.R. Hill and G.E. Ioup. Convergence of the Van Cittert iterative method of deconvolution.Journal of the Optical Society America, Vol. 66, pp. 487–489, 1976.

[611] K. Hirano, M. Sakane, and M.Z. Mulk. Design of 3–D Recursive Digital Filters. IEEETransactions Circuits and Systems, Vol. 31, pp. 550–561, 1984.

[612] E.W. Hobson. The theory of functions of a real variable and the theory of Fourier’sseries. Michigan Historical Reprint Series. Scholarly Publishing Office, University of MichiganLibrary, 2005.

[613] Robert V. Hogg,Allen Craig, and Joseph W. McKean. Introduction to Mathematical Statistics(6th Edition). Prentice Hall, 2004.

[614] E. Holzler. Some remarks on special cases of the sampling theorem. Frequenz, Vol. 31,pp. 265–269, 1977.

[615] I. Honda. Approximation for a class of signal functions by sampling series representation. KeioEngineering Rep., Vol. 31, pp. 21–26, 1978.

[616] I. Honda.An abstraction of Shannon’s sampling theorem. IEICE Transactions on Fundamentalsof Electronics Communications and Computer Sciences, Vol. E81A(6), pp. 1187–1193, 1998.

[617] W. Hoppe. The finiteness postulate and the sampling theorem of the three dimensional electronmicroscopical analysis of aperiodic structures. Optik, Vol. 29, pp. 619–623, 1969.

[618] H. Horiuchi. Sampling principle for continuous signals with time-varying bands. Information &Control, Vol. 13, pp. 53–61, 1968.

[619] Lars Hörmander. An Introduction to Complex Analysis in Several Variables. Van Nostrand,Princeton, NJ, 1966.

[620] Lars Hörmander. The Analysis of Linear Partial Differential Operators I: DistributionTheory and Fourier Analysis. Springer, 2003.

[621] R.F. Hoskins and J.S. Pinto. Generalized sampling expansion in the sense of Papoulis. SIAMJ. Applied Math., Vol. 44, pp. 611–617, 1984.

[622] R.F. Hoskins and J.S. Pinto. Sampling expansions and generalized translation invariance.Journal Franklin Institute, Vol. 317, pp. 323–332, 1984.

[623] G.H. Hostetter. Generalized interpolation of continuous-time signal samples. IEEETransactionsSystems, Man, Cybernetics, Vol. SMC-11, pp. 433–439, 1981.

[624] S.J. Howard. Continuation of discrete Fourier spectra using minimum-negativity constraintJournal of the Optical Society America, Vol. 71, pp. 819–824, 1981.

[625] S.J. Howard. Method for continuing Fourier spectra given by the fast Fourier transform. Journalof the Optical Society America, Vol. 71, pp. 95–98, 1981.


REFERENCES 705

[626] S.J. Howard. Fast algorithm for implementing the minimum-negativity constraint for Fourierspectrum extrapolation. Applied Optics, Vol. 25, pp. 1670–1675, 1986.

[627] Kenneth B. Howell. Principles of Fourier Analysis. CRC, 2001.[628] P. Hoyer. Simplified proof of the Fourier Sampling Theorem. Information Processing Letters,

Vol. 75(4), pp. 139–143, 2000.[629] T.C. Hsiah. Comparisons of adaptive sampling control laws. IEEE Transactions Automatic

Control, Vol. AC-17, pp. 830–831, 1972.[630] T.C. Hsiah. Analytic design of adaptive sampling control law in sampled data systems. IEEE

Transactions Automatic Control, Vol. 19, pp. 39–41, 1974.[631] Hwei Hsu. Applied Fourier Analysis. Harcourt Brace Jovanovich, 1984.[632] Y. Hu, K.D.K. Luk, W.W. Lu, A. Holmes, and J.C.Y. Leong. Comparison of time-frequency

distribution techniques for analysis of spinal somatosensory evoked potential. Medical &Biological Engineering & Computing, Vol. 39(3), pp. 375–380, 2001.

[633] Hua Huang, Xin Fan, Chun Qi, and Shi-Hua Zhu. A learning-based POCS algorithm forface image super-resolution reconstruction. Proceedings of 2005 International Conference onMachine Learning and Cybernetics, Vol. 8, pp. 5071–5076, 2005.

[634] E.X. Huang and A.K. Fung, An application of sampling theorem to moment methodsimulation in surface scattering. Journal of ElectromagneticWaves and Applications, Vol. 20(4),pp. 531–546, 2006.

[635] F.O. Huck, N. Halyo, and S.K. Park. Aliasing and blurring in 2-D sampled imagery. AppliedOptics, Vol. 19, pp. 2174–2181, 1980.

[636] F.O. Huck and S.K. Park. Optical-mechanical line-scan imaging process: Its informationcapacity and efficiency. Applied Optics, Vol. 14, pp. 2508–2520, 1975.

[637] A. Hughes. Cat retina and the Sampling Theorem-the Relation of Transient and SustainedBrisk Unit Cutoffs Frequency to Alpha Mode and Beta Node Cell Density. Experimental BrainResearch, Vol. 42(2), pp. 196–202, 1981.

[638] R. Hulthen. Restoring causal signals by analytic continuation: A generalized sampling theoremfor causal signals. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-31,pp. 1294–1298, 1983.

[639] H.E. Hurzeler. The Optional Sampling Theorem for Processes Indexed by a Partially OrderedSet. Annals Of Probability, Vol. 13(4), pp. 1224–1235, 1985.

I[640] Y. Ichioka and N. Nakajima. Iterative image restoration consideration visibility. Journal of the

Optical Society America, Vol. 71, pp. 983–988, 1981.[641] O. Ikeda and T. Sato. Super-resolution imaging system using waves with a limited frequency

bandwidth. Journal Acoust. Society America, Vol. 6, pp. 75–81, 1979.[642] Inna V. Ilyina, Alexander S. Sobolev, and Tatyana Yu. Cherezova; Alexis V. Kudryashov.

Gerchberg-Saxton Iterative Algorithm for Flexible Mirror Performance. 8-th InternationalConference on Laser and Fiber-Optical Networks Modeling. pp. 442–445, 2006.

[643] G. Indebetow. Propagation of spatially periodic wavefields. Opt. Acta., pp. 531–539, 1984.[644] G. Indebetow. Polychromatic self-imaging. Journal Mod. Opt., pp. 243–252, 1988.[645] Leopold Infeld. Quest: The Evolution of a Scientist. Doubleday, Doran (1941). Reprinted

Transaction Pub, 1990.[646] Valéria de Magalhaes Iorio. Fourier Analysis and Partial Differential Equations: An

Introduction. Cambridge University Press, 2001.[647] H. Ishida, Fourier Transform–Infrared Characterization of Polymers. Springer, 1987.[648] M.E. Ismail andAhmed I. Zayed.Aq-analogue of the Whittaker-Shannon-Kotelnikov sampling

theorem. Proceedings of the American Mathematical Society, Vol. 131(12), pp. 3711–3719,2003.

[649] S.H. Izen. Generalized sampling expansion on lattices. IEEE Transactions of Signal Processing,Vol. 53(6), pp. 1949–1963, 2005.

[650] Leland B. Jackson. Digital Filters and Signal Processing... with MATLAB Exercises,Springer; 3 edition 1995.


706 REFERENCES

[651] Dunham Jackson. Fourier Series and Orthogonal Polynomials. Dover Publications, 2004.[652] J.F. James. A Student’s Guide to Fourier Transforms. Cambridge University Press; 2 edition,

2002.

J[653] M.A. Jack, P.M. Grant, and J.H. Collins. The theory, design, and applications of surface acoustic

wave Fourier-transform processors. Proceedings of the IEEE, Vol. 68(4), pp. 450–468, 1980.[654] J.S. Jaffe. Limited angle reconstruction using stabilized algorithms. IEEE Transactions on

Medical Imaging, Vol. 9(3), pp. 338–344, 1990.[655] D.L. Jagerman. Bounds for truncation error of the sampling expansion. SIAM J. Applied Math.,

Vol. 14, pp. 714–723, 1966.[656] D.L. Jagerman. Information theory and approximation of bandlimited functions. Bell Systems

Tech. J., Vol. 49, pp. 1911–1941, 1970.[657] D.L. Jagerman and L. Fogel. Some general aspects of the sampling theorem. IRE Transactions

Information Theory, Vol. IT-2, pp. 139–146, 1956.[658] J. Jahns and A.W. Lohmann. The Lau effect (a diffraction experiment with incoherent

illumination). Optical Communication, pp. 263–267, 1979.[659] A.K. Jain. Fundamentals of Digital Image Processing. Prentice-Hall, Englewood Cliffs, NJ,

1989.[660] A.K. Jain and S. Ranganath. Extrapolation algorithms for discrete signals with application

to spectral estimation. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-29,pp. 830–845, 1981.

[661] S. Jang, W. Choi, T.K. Sarkar, M. Salazar-Palma, K. Kyungjung, and C.E. Baum. Exploitingearly time response using the fractional Fourier transform for analyzing transient radar returns.IEEE Transactions on Antennas and Propagation, Vol. 52(11), pp. 3109–3121, 2004.

[662] T. Jannson. Shannon number of an image and structural information capacity in volumeholography. Opt. Acta, pp. 1335–1344, 1980.

[663] A.J.E.M. Janssen. Weighted Wigner distributions vanishing on lattices. Journal Math. Anal.Applied, Vol. 80, pp. 156–167, 1981.

[664] A.J.E.M. Janssen. Gabor representation of generalized functions. Journal Math. Anal. Applied,Vol. 83, pp. 377–396, 1981.

[665] A.J.E.M. Janssen. Positivity of weighted Wigner distributions. SIAM J. Math. Anal., Vol. 12,pp. 752–758, 1981.

[666] A.J.E.M. Janssen. Bargmann transform, Zak transform and coherent states. Journal Math.Phys., Vol. 23, pp. 720–731, 1982.

[667] A.J.E.M. Janssen. The Zak transform: a signal transform for sampled time-continuous signals.Philips J. Res., Vol. 43, pp. 23–69, 1988.

[668] A.J.E. Janssen, R.N. Veldhuis, and L.B. Vries. Adaptive interpolation of discrete time signalsthat can be modeled as autoregressive processes. IEEE Transactions Acoust., Speech, SignalProcessing, Vol. ASSP-34, pp. 317–330, 1986.

[669] P.A. Jansson, editor. Deconvolution. With applications in Spectroscopy. Academic Press,Orlando, FL, 1984.

[670] P.A. Jansson, R.H. Hunt, and E.K. Plyer. Resolution enhancement of spectra. Journal of theOptical Society America, Vol. 60, pp. 596–599, 1970.

[671] Y.C. Jenq. Digital spectra of nonuniformly sampled signals: Digital look up tunable sinusoidaloscillators. IEEE Transactions Instrumentation & Measurement, Vol. 37, No. 3, pp. 358–362,1988.

[672] Yeonsik Jeong, Inkyeom Kim, and Hyunchul Kang. A practical projection-based postprocess-ing of block-coded images with fast convergence rate. IEEE Transactions on Circuits andSystems for Video Technology, Vol. 10(4), pp. 617–623, 2000.

[673] A.J. Jerri. On the application of some interpolating functions in physics. Journal Res. NationalBureau of Standards -B. Math. Sciences, Vol. 73B, No. 3, pp. 241–245, 1969.

[674] A.J. Jerri. On the equivalence of Kramer’s and Shannon’s generalized sampling theorems. IEEETransactions Information Theory, Vol. IT-15, pp. 469–499, 1969.


REFERENCES 707

[675] A.J. Jerri. Some applications for Kramer’s generalized sampling theorem. Journal EngineeringMath., Vol. 3, No. 2, April 1969.

[676] A.J. Jerri. Application of the sampling theorem to time-varying systems. Journal FranklinInstitute, Vol. 293, pp. 53–58, 1972.

[677] A.J. Jerri. Sampling for not necessarily finite energy signals. International J. System Sci., Vol. 4,No. 2, pp. 255–260, 1973.

[678] A.J. Jerri. Sampling expansion for the Lαν -Laguerre integral transform. Journal Res. NationalBureau of Standards -B. Math. Sciences, Vol. 80B, pp. 415–418, 1976.

[679] A.J. Jerri. The Shannon sampling theorem-its various extensions and applications: A tutorialreview. Proceedings IEEE, Vol. 65, No. 11, pp. 1565–1596, 1977.

[680] A.J. Jerri. Computation of the Hill functions of higher order. Math. Comp., Vol. 31, pp. 481–484,1977.

[681] A.J. Jerri. Towards a discrete Hankel transform and its applications. Journal of Applied Anal.,Vol. 7, pp. 97–109, 1978.

[682] A.J. Jerri. The application of general discrete transforms to computing orthogonal series andsolving boundary value problems. Bull. Calcutta Math. Society, Vol. 71, pp. 177–187, 1979.

[683] A.J. Jerri. General transforms hill functions. Journal Applicable Analysis, Vol. 14, pp. 11–25,1982.

[684] A.J. Jerri. A note on sampling expansion for a transform with parabolic cylinder kernel. Inform.Sci., Vol. 26, pp. 1–4, 1982.

[685] A.J. Jerri. On a recent application of the Shannon sampling theorem. In IEEE InternationalSymposium on Information Theory, Quebec, Canada, 1983.

[686] A.J. Jerri. A definite integral. SIAM Rev., Vol. 25, No.1, p. 101, 1983.[687] A.J. Jerri. Interpolation for the generalized sampling sum of approximation theory. The AMS

Summer Meeting, Albany, NY, 1983.[688] A.J. Jerri. Application of the transform–iterative method to nonlinear concentration boundary

value problem. Chem. Engineering Commun., Vol. 23, pp. 101–113, 1983.[689] A.J. Jerri. The generalized sampling theorem for transforms of not necessarily square integrable

functions. Journal Math., Math. Sci., Vol. 8, pp. 355–358, 1985.[690] A.J. Jerri. Introduction to Integral Equations with Applications. Marcel Dekker, New York,

1985.[691] A.J. Jerri. Part II: The Sampling Expansion – A Detailed Bibliography. 1986.[692] A.J. Jerri. An extended Poisson type sum formula for general integral transforms and

aliasing error bound for the generalized sampling theorem. Journal Applied Analysis, Vol. 26,pp. 199–221, 1988.

[693] A.J. Jerri. The Gibbs Phenomenon in FourierAnalysis, Splines and Wavelet. Springer, 1998.[694] A.J. Jerri.Arecent modification of iterative methods for solving nonlinear problems. The Math.

Heritage of C.F. Gauss, 1991, G.M. Rassias, editor, World Scientific Publ. Co., Singapore,pp. 379–404.

[695] A.J. Jerri. Integral and Discrete Transforms with Applications and Error Analysis. MarcelDekker Inc., New York, 1992.

[696] A.J. Jerri and E.J. Davis. Application of the sampling theorem to boundary value problems.Journal Engineering Math., Vol. 8, pp. 1–8, 1974.

[697] A.J. Jerri and D.W. Kreisler. Sampling expansions with derivatives for finite Hankel and othertransforms. SIAM J. Math. Anal., Vol. 6, pp. 262–267, 1975.

[698] A.J. Jerri. Truncation error for the generalized Bessel type sampling series. Journal FranklinInstitute (USA) Vol. 314, No. 5, pp. 323–328, 1982.

[699] A.J. Jerri, R.L. Herman and R.H. Weiland. A modified iterative method for nonlinear chemicalconcentration in cylindrical and spherical pellets. Chem. Engineering Commun., Vol. 52,pp. 173–193, 1987.

[700] H. Johnen. Inequalities connected with moduli of smoothness. Mat. Vesnik, Vol. 9(24),pp. 289–303, 1972.

[701] G. Johnson and J.H.S. Hutchinson. The limitations of NMR recalled–echo imaging techniques.Journal Magnetic Resonance, Vol. 63, pp. 14–30, 1985.


708 REFERENCES

[702] Joint Photographic Experts Group, ISO-IEC/JTC1/SC2/WP8, “JPEG technical specification,revision 8,” JPEG-8-R8, 1990.

[703] M.C. Jones. The discrete Gerchberg algorithm. IEEE Transactions Acoust., Speech, SignalProcessing, Vol. ASSP-34, pp. 624–626, 1986.

[704] D.L. Jones, R.G. Baraniuk. An adaptive optimal-kernel time-frequency representation. IEEETransactions on Signal Processing, Vol. 43(10), pp. 2361–2371, 1995.

[705] I.I. Jouny. Scattering analysis using fractional Fourier with applications in mine detection.Proceedings. 2004 IEEE International Geoscience and Remote Sensing Symposium, 2004.IGARSS ’04. Vol. 5, pp. 3460–3463, 2004.

K[706] M. Kac, W.L. Murdock, and G. Szegö. On the eigenvalues of certain Hermitian forms. Journal

Rat. Mech., Anal., pp. 767–800, 1953.[707] M.I. Kadec. The exact value of the Paley-Wiener constant Soviet Math. Dokl., Vol. 5,

pp. 559–561, 1964.[708] R.E. Kahn and B. Liu. Sampling representation and optimum reconstruction of signals. IEEE

Transactions Information Theory, Vol. IT-11, pp. 339–347, 1965.[709] T. Kailath. Channel characterization: time-variant dispersive channels. In Lectures on

Communications Systems Theory, E.J. Baghdady, editor, McGraw-Hill, New York, 1960.[710] S.C. Kak. Sampling theorem in Walsh-Fourier analysis. Electron. Letters, Vol. 6,

pp. 447–448, 1970.[711] Avinash C. Kak, Malcolm Slaney. Principles of Computerized Tomographic Imaging.

Industrial & Applied Math (2001).[712] G. Kakoza and D. Munson. A frequency-domain characterization of interpolation from

nonuniformly spaced data. In Proceedings of the International Symposium on Circuits andSystems, Portland, Oregon, pp. 288–291, 1989.

[713] F. Kamalabadi and B. Sharif. Robust regularized tomographic imaging with convex projections.IEEE International Conference on Image Processing, 2005. ICIP 2005. Vol. 2, pp. II - 205–208,2005.

[714] N.S. Kambo and F.C. Mehta. Truncation error for bandlimited non-stationary processes. Inform.Sci., Vol. 20, pp. 35–39, 1980.

[715] N.S. Kambo and F.C. Mehta. An upper bound on the mean square error in the samplingexpansion for non-bandlimited processes. Inform. Sci., Vol. 21, pp. 69–73, 1980.

[716] E.O. Kamenetskii. Sampling theorem in macroscopic electrodynamics of crystal lattices.Physical Review E, Vol. 57(3), pp. 3556–3562, Part B, 1998.

[717] David W. Kammler. First Course in Fourier Analysis. Prentice Hall, 2000.[718] M. Kato, I. Yamada and K. Sakaniwa. A set-theoretic blind image deconvolution based

on hybrid steepest descent method. IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences. Vol. E82A (8), pp. 1443–1449, 1999.

[719] K. Kazimierczuk, W. Kozminski, and I. Zhukov. Two-dimensional Fourier transform of arbi-trarily sampled NMR data sets. Journal of Magnetic Resonance,Vol. 179(2), pp. 323–328, 2006.

[720] L.M. Kani and J.C. Dainty. Super-resolution using the Gerchberg algorithm. OpticalCommunication, pp. 11–17, 1988.

[721] D. Kaplan and R.J. Marks II. Noise sensitivity of interpolation and extrapolation matrices.Applied Optics, Vol. 21, pp. 4489–4492, 1982.

[722] Saleem A. Kassam. Signal Detection in Non-Gaussian Noise. Springer-Verlag, 1988.[723] R. Kasturi, T.T. Krile, and J.F. Walkup. Space-variant 2-D processing using a sampled input/

sampled transfer function approach. SPIE Inter. Optical Comp. Conf., Vol. 232, pp. 182–190,1980.

[724] Jyrki Kauppinen and Jari Partanen. Fourier Transforms in Spectroscopy. Wiley, 2001.[725] M. Kawamura and S. Tanaka. Proof of sampling theorem in sequency analysis using extended

Walsh functions. Systems-Comput. Controls, Vol. 9, pp. 10–15, 1980.[726] Steven M. Kay. The effect of sampling rate on autocorrelation estimation. IEEE Transactions

Acoust., Speech, Signal Processing, Vol. ASSP-29, No. 4, p. 859–867, 1981.


REFERENCES 709

[727] R.B. Kerr. Polynomial interpolation errors for bandlimited random signals. IEEE TransactionsSystems, Man, Cybernetics, pp. 773–774, 1976.

[728] R.B. Kerr. Truncated sampling expansions for bandlimited random signals. IEEE TransactionsSystems, Man, Cybernetics, Vol. SMC-9, pp. 362–364, 1979.

[729] L.M. Khadra, J.A. Draidi, M.A. Khasawneh and M.M. Ibrahim. Time-frequency distributionsbased on generalized cone-shaped kernels for the representation of nonstationary signals.Journal of the Franklin Institute-Engineering and Appled Mathematics. Vol. 335B(5),pp. 915–928, 1998.

[730] K. Khare and N. George. Sampling-theory approach to eigenwavefronts of imagingsystems.Journal of the Optical Society of America A-Optics, Image Science and Vision,Vol. 22(3), pp. 434–438, 2005.

[731] K. Khare. Bandpass sampling and bandpass analogues of prolate spheroidal functions. SignalProcessing, Vol. 86(7), pp. 1550–1558, 2006.

[732] A.A. Kharkevich. Kotelnikov’s theorem-a review of some new publications. Radiotekhnika,Vol. 13, pp. 3–10, 1958.

[733] Y.I. Khurgin and V.P. Yakovlev. Progress in the Soviet Union on the theory and applications ofbandlimited functions. Proceedings IEEE, Vol. 65, pp. 1005–1029, 1976.

[734] T. Kida. Generating functions for sampling theorems. Electronics and Communications inJapan, (English Translation), Vol. 65(1), pp. 9–18, 1982.

[735] T. Kida. Extended formulas of sampling theorem on bandlimited waves and their applicationto the design of digital filters for data transmission. Electron Communication Japan, Part 1,Vol. 68(11), pp. 20–29, 1985.

[736] Yoon Kim, Chun-Su Park and Sung-Jea Ko. Fast POCS based post-processing technique forHDTV. IEEE Transactions on Consumer Electronics, Vol. 49(4), pp. 1438–1447, 2003.

[737] Yoon Kim, Chun-Su Park, Sung-Jea Ko. Frequency domain post-processing technique basedon POCS. Electronics Letters, Vol. 39(22), pp. 1583–1584, 2003.

[738] G.W. King and A.G. Emslie. Spectroscopy from the point of view of the communication theoryI. Journal of the Optical Society America, Vol. 41, pp. 405–409, 1951.

[739] G.W. King and A.G. Emslie. Spectroscopy from the point of view of the communication theoryIII. Journal of the Optical Society America, Vol. 43, pp. 664–668, 1953.

[740] K. Kinoshita and M. Lindenbaum. Robotic control with partial visual information. InternationalJournal of Computer Vision, Vol. 37(1), pp. 65–78, 2000.

[741] J.G. Kirkwood. Quantum statistics if almost classical ensembles. Phys. Rev., Vol.44, pp. 31–37,1933.

[742] S.J. Kishner and T.W. Barnard. Detection and location of point images in sampled opticalsystems. Journal of the Optical Society America, Vol. 62, pp. 17–20, 1972.

[743] Morris Kline. Mathematical Thought from Ancient to Modern Times, Oxford UniversityPress, 1972.

[744] D. Klusch. The Sampling Theorem, Dirichlet Series and Hankel Transforms. Journal ofComputational and Applied Mathematics, Vol. 44(3), pp. 261–273, 1992.

[745] I. Kluvanek. Sampling theorem in abstract harmonic analysis. Mat. Casopis Sloven. Akad. Vied,Vol. 15, pp. 43–48, 1965.

[746] J.J. Knab. System error bounds for Lagrange estimation of bandlimited functions. IEEETransactions Information Theory, Vol. IT-21, pp. 474–476, 1975.

[747] J.J. Knab. Interpolation of bandlimited functions using the approximate prolate series. IEEETransactions Information Theory, Vol. IT-25, pp. 717–720, 1979.

[748] J.J. Knab. Simulated cardinal series errors versus truncation error bounds. Proceedings IEEE,Vol. 68, pp. 1020–1060, 1980.

[749] J.J. Knab. Noncentral interpolation of bandlimited signals. IEEE Transactions Aerospace &Electronic Systems, Vol. AES-17, pp. 586–591, 1981.

[750] J.J. Knab and M.I. Schwartz. A system error bound for self truncating reconstruction filterclass. IEEE Transactions Information Theory, Vol. IT-21, pp. 341–342, 1975.

[751] I.P. Knyshev. The sampling theorem in amplitude, quantization of random signals. Journal ofCommunications Technology and Electronics, Vol. 47(12), pp. 1361–1363, 2002.


710 REFERENCES

[752] I.P. Knyshev. The sampling theorem in amplitude, quantization of random signals. Journal ofCommunications Technology and Electronics, Vol. 47(12), pp. 1361–1363, 2002.

[753] Y. Kobayashi and M. Inoue. Combination of two discrete Fourier transforms of data sampledseparately at different rates. Journal Inf. Process, Vol. 3, pp. 203–207, 1980.

[754] T. Kodama. Sampling theorem application to SAW diffraction simulation. Electron. Letters,Vol. 16, pp. 460–462, 1980.

[755] H. Kogelnik and T. Li. Laser beams and resonators. Proceedings IEEE, pp. 1312–1329,1966.

[756] A. Kohlenberg. Exact interpolation of bandlimited functions. Journal Applied Phys., Vol. 24,pp. 1432–1436, 1953.

[757] D. Kohler and L. Mandel. Source reconstruction from the modulus of the correlation function:a practical approach to the phase problem of optical coherence theory. Journal of the OpticalSociety America, Vol. 63, pp. 126–134, 1973.

[758] K. Kojima. Sampling Theorem in Diffraction Integral Transform. Japanese Journal of AppliedPhysics, Vol. 16(5), pp. 817–825, 1977.

[759] Chi-Wah Kok; Man-Wai Kwan. Sampling theorem for ISI-free communication. Proceedings.IEEE International Symposium on Information Theory, p. 99, 2003.

[760] Alexander Koldobsky. Fourier Analysis In Convex Geometry. American MathematicalSociety 2005.

[761] A.N. Kolmogorov. Interpolation und Extrapolation von stationären zufälligen Folgen (Russian).Bull Acad. Sci. USSR, Ser. Math, Vol. 5, pp. 3–14, 1941.

[762] B.H. Kolner and D.M. Bloom. Direct electric-optic sampling of transmission-line signalspropagating on a GaAs substrate. Electron. Letters, Vol. 20, pp. 818–819, 1984.

[763] A. Kolodziejczyk. Lensless multiple image formation by using a sampling filter. OpticalCommunication, pp. 97–102, 1986.

[764] Vilmos Komornik and Paola Loreti. Fourier Series in Control Theory. Springer, 2005.[765] R. Konoun. PPM reconstruction using iterative techniques, project report. Technical report,

Dept. of ECE, Illinois Institute of Technology, Chicago, September, 1989.[766] P. Korn. Some uncertainty principles for time-frequency transforms of the Cohen class. IEEE

Transactions on Signal Processing, Vol. 53(2), Part 1, pp. 523–527, 2005.[767] T.W. Körner. Fourier Analysis. Cambridge University Press; Reprint edition, 1989.[768] A. Korpel. Gabor: frequency, time and memory. Applied Optics, pp. 3624–3632, 1982.[769] Z. Kostic. Low-complexity equalization for π

4 DQPSK signals based on the methodof projection onto convex sets. IEEE Transactions on Vehicular Technology, Vol. 48(6),pp. 1916–1922, 1999.

[770] V.A. Kotelnikov. On the carrying capacity of “ether” and wire in electrocommunications. In Idz.Red. Upr. Svyazi RKKA(Moscow), Material for the first all-union conference on the questionsof communications, 1933.

[771] K.T. Kou and T. Qian. Shannon sampling and estimation of band-limited functions in the severalcomplex variables setting. Acta Mathematica Scientia, Vol. 25(4), pp. 741–754, 2005.

[772] H.P. Kramer. A generalized sampling theorem. Journal Math. Phys., Vol. 38, pp. 68–72, 1959.[773] H.P. Kramer. The digital form of operators on bandlimited functions. Journal Math. Anal.

Applied, Vol. 44, No. 2, pp. 275–287, 1973.[774] G.M. Kranc. Comparison of an error-sampled system by a multirate controller. Transactions

America Institute Elec. Engineering, Vol. 76, pp. 149–159, 1957.[775] E. Krasnopevtsev. Fractional Fourier transform based on geometrical optics Proceedings

KORUS 2003. The 7th Korea-Russia International Symposium on Science and Technology,Vol. 3, pp. 82–86, 2003.

[776] M.G. Krein. On a fundamental approximation problem in the theory of extrapolation andfiltration of stationary random processes (Russian). Dokl. Akad. Nauk SSSR Vol. 94, pp. 13–16,1954. [English translation: Amer. Math. Society Selected Transl. Math. Statist. Prob. 4,pp. 127–131], 1964.

[777] R. Kress. On the general Hermite cardinal interpolation. Math. Comput., Vol. 26, pp. 925–933,1972.


REFERENCES 711

[778] H.N. Kritikos and P.T. Farnum. Approximate evaluation of Gabor expansions. IEEETransactions Syst., Man, Cybern. SMC-17, pp. 978–981, 1987.

[779] J.W. Krutch. “The Colloid and the Crystal”, in I. Gordon and S. Sorkin (eds.) The ArmchairScience Reader, New York: Simon and Schuster, 1959.

[780] A. Kumar and O.P. Malik. Discrete analysis of load-frequency control problem. ProceedingsIEEE, Vol. 131, pp. 144–145, 1984.

[781] H.R. Kunsch, E. Agrell and F.A. Hamprecht. Optimal lattices for sampling. IEEE Transactionson Information Theory, Vol. 51(2), pp. 634–647, 2005.

[782] G.M. Kurajian and T.Y. Na. Elastic beams on nonlinear continuous foundations. ASME WinterAnnual Meeting, pp. 1–7, 1981.

[783] T.G. Kurtz. The Optional Sampling Theorem for Martengales Indexed by Directed Sets. Annalsof Probability, Vol. 8(4), pp. 675–681, 1980.

[784] H.J. Kushner and L. Tobias. On the stability of randomly sampled systems. IEEE TransactionsAutomatic Control, Vol. AC-14, pp. 319–324, 1969.

[785] A. Kutay, H.M. Ozaktas, O. Ankan, and L. Onural. Optimal filtering in fractional Fourierdomains. IEEE Transactions on Signal Processing, Vol. 45(5), pp. 1129–1143, 1997.

[786] Goo-Rak Kwon, Hyo-Kak Kim, Yoon Kim and Sung-Jea Ko. An efficient POCS-based post-processing technique using wavelet transform in HDTV. IEEE Transactions on ConsumerElectronics, Vol. 51(4), pp. 1283–1290, 2005.

[787] M.S. Kwon,Y.B. Cho and S.Y. Shin. Experimental demonstration of a long-period grating basedon the sampling theorem. Applied Physics Letters, Vol. 88(21), Art. No. 211103, 22 2006.

[788] M.S. Kwon and S.Y. Shin. Theoretical investigation of a notch filter using a long-period gratingbased on the sampling theorem. Optics Communications, Vol. 263(2), pp. 214–218, 2006.

L[789] B. Lacaze. A generalization of n-th sampling formula. Ann. Telecomm., Vol. 30, pp. 208–210,

1975.[790] P. Lancaster and M. Tiemenesky. The Theory of Matrices. Academic Press, Orlando, FL,

1985.[791] H.J. Landau. On the recovery of a bandlimited signal after instantaneous companding and

subsequent band limiting. Bell Systems Tech. J., Vol. 39, pp. 351–364, 1960.[792] H.J. Landau. Necessary density conditions for sampling and interpolation of certain entire

functions. Acta Math., pp. 37–52, 1967.[793] H.J. Landau. Sampling, data transmission and the Nyquist rate. Proceedings IEEE, Vol. 55,

pp. 1701–1706, 1967.[794] H.J. Landau. On Szegö’s eigenvalue distribution theorem and non-Hermitian kernels. Journal

Analyse Math., pp. 335–357, 1975.[795] H.J. Landau and W.L. Miranker. The recovery of distorted bandlimited signals. Journal Math.

Anal. & Applied, Vol. 2, pp. 97–104, 1961.[796] H.J. Landau and H.O. Pollak. Prolate spheroidal wave functions Fourier analysis and

uncertainty II. Bell Systems Tech. J., Vol. 40, pp. 65–84, 1961.[797] H.J. Landau and H.O. Pollak. Prolate spheroidal wave functions Fourier analysis and

uncertainty III: The dimension of the space of essentially time- and bandlimited signals. BellSystems Tech. J., Vol. 41, pp. 1295–1336, 1962.

[798] H.J. Landau and H. Widom. Eigenvalue distribution of time and frequency limiting. JournalMath. Anal., Applied, Vol. 77, pp. 469–481, 1980.

[799] A. Landé. Optik und Thermodynamik, In Handbuch der Physik, Springer-Verlag, Berlin,pp. 453–479, 1928.

[800] L. Landweber. An iteration formula for Fredholm integral equations of the first kind.Amer. J. Math., pp. 615–624, 1951.

[801] P.J. La Riviere and X.C. Pan. Interlaced interpolation weighting functions for multislice helicalcomputed tomography. Optical Engineering, Vol. 42(12), pp. 3461–3470, 2003.

[802] Rupert Lasser. Introduction to Fourier Series. CRC, 1996.[803] B.P. Lathi. Communication Systems. John Wiley & Sons, Inc., New York, 1965.


712 REFERENCES

[804] K.N. Le, K.P. Dabke and G.K. Egan. Signal detection using time-frequency distributions withnonunity kernels. Optical Engineering, Vol. 40(12), pp. 2866–2877, 2001.

[805] Thuyen Le and M. Glesner. Rotating stall analysis using signal-adapted filter bank and Cohen’stime-frequency distributions. Proceedings of the 2000 IEEE International Symposium onCircuits and Systems, ISCAS 2000 Geneva. Vol. 1, 28–31, pp. 603–606, 2000.

[806] A.J. Lee. On bandlimited stochastic processes. SIAM J. Applied Math., Vol. 30, pp. 269–277,1976.

[807] A.J. Lee. Approximate interpolation and the sampling theorem. SIAM J. Applied Math., Vol. 32,pp. 731–744, 1977.

[808] A.J. Lee. Sampling theorems for nonstationary random processes. Transactions Amer. Math.Society, Vol. 242, pp. 225–241, 1978.

[809] A.J. Lee. A note on the Campbell sampling theorem. SIAM J. Applied Math., Vol. 41,pp. 553–557, 1981.

[810] H. Lee. On orthogonal transformations. IEEE Transactions Circuits & Systems, Vol. CAS-32,pp. 1169–1177, 1985.

[811] Y.W. Lee. Statistical Theory of Communication. John Wiley & Sons, New York, 1960.[812] W.H. Lee. Computer-generated holograms: techniques and applications, In Progress in Optics,

North-Holland, Amsterdam, 1978, pp. 119–232.[813] A.J. Lee. Approximate Interpolation and Sampling Theorem. SIAM Journal on Applied

Mathematics, Vol 32(4), pp. 731–744 1977.[814] S. Lee, P.S. Cho, R.J. Marks II, and S. Oh. Conformal radiotherapy computation by the

method of alternating projection onto convex sets. Phys. Med. Biol., Vol. 42, pp. 1065–1086,1997.

[815] X. Lee, Y.-Q. Zhang, and A. Leon-Garcia. Information loss recovery for block-based Imagecoding techniques-A fuzzy logic approach. IEEE Transactions Image Processing, Vol. 4,pp. 259–273, 1995.

[816] J. Leibrich and H. Puder. A TF distribution for disturbed and undisturbed speech signals andits application to noise reduction. Signal Processing. Vol. 80(9), pp. 1761–1776, 2000.

[817] E.N. Leith and J. Upatnieks. Reconstructed wavefronts and communication theory. Journal ofthe Optical Society America, pp. 1123–1130, 1962.

[818] O.A.Z. Leneman. Random sampling of random processes: impulse processes. Information &Control, Vol. 9, pp. 347–363, 1966.

[819] O.A.Z. Leneman. On error bounds for jittered sampling. IEEE Transactions Automatic Control,Vol. AC-11, p. 150, 1966.

[820] O.A.Z. Leneman. Random sampling of random processes: optimum linear interpolation.Journal Franklin Institute, Vol. 281, pp. 302–314, 1966.

[821] O.A.Z. Leneman and J. Lewis. A note on reconstruction for randomly sampled data. IEEETransactions Automatic Control, Vol. AC-10, p. 626, 1965.

[822] O.A.Z. Leneman and J. Lewis. Random sampling of random processes: Mean squarecomparison of various interpolators. IEEE Transactions Automatic Control, Vol. AC-10,pp. 396–403, 1965.

[823] O.A.Z. Leneman and J. Lewis. On mean-square reconstruction error. IEEE TransactionsAutomatic Control, Vol. AC-11, pp. 324–325, 1966.

[824] A. Lent and H. Tuy. An iterative method for the extrapolation of bandlimited functions. JournalMath. Anal., Applied, pp. 554–565, 1981.

[825] J. LeRoux, P. Lise, E. Zerbib, et al. A formulation in concordance with the sampling theoremfor band-limited images reconstruction from projections. Multidimensional Systems and SignalProcessing, Vol. 7(1), pp. 27–52, 1996.

[826] Pete E. Lestrel (Editor). Fourier Descriptors and their Applications in Biology. CambridgeUniversity Press, 1997.

[827] Emmanuel Letellier. Fourier Transforms of Invariant Functions on Finite Reductive LieAlgebras. Springer, 2005.

[828] L. Levi. Fitting a bandlimited signal to given points. IEEE Transactions Information Theory,Vol. IT-11, pp. 372–376, 1965.


REFERENCES 713

[829] N. Levinson. Gap and density theorems. In Colloq. Pub. 26. Amer. Math. Society, New York,1940.

[830] M. Levonen and S. McLaughlin. Fractional Fourier transform techniques applied to activesonar. Proceedings OCEANS 2003. Vol. 4, pp. 1894–1899, 2003.

[831] Jian Li and Petre Stoica. Robust Adaptive Beamforming. Wiley-Interscience, 2005.[832] G.B. Lichtenberger. A note on perfect predictability and analytic processes. IEEE Transactions

Information Theory, Vol. IT-20, pp. 101–102, 1974.[833] B. Lien and G. Tang. Reversed Chebyshev implementation of McClellan transform and its

roundoff error. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 35(10),pp. 1435–1439, 1987.

[834] A. Wee-Chung Liew and Hong Yan. POCS-based blocking artifacts suppression with regionsmoothness constraints for graphic images. Proceedings of 2004 International Symposium onIntelligent Multimedia, Video and Speech Processing, pp. 563–566, 2004.

[835] Y. Linde, A. Buzo and R.M. Gray. An algorithm for vector quantizer design. IEEE TransactionsCommun., Vol. COM-28, pp. 89–95, 1980.

[836] D.A. Linden. A discussion of sampling theorems. Proceedings IRE, Vol. 47, pp. 1219–1226,1959.

[837] D.A. Linden and N.M. Abramson. A generalization of the sampling theorem. Information &Control, Vol. 3, pp. 26–31, 1960.

[838] E.H. Linfoot. Information theory and optical images. Journal of the Optical Society America,pp. 808–819, 1955.

[839] E.H. Linfoot. Quality evaluation of optical systems. Opt. Acta, pp. 1–14, 1958.[840] John Litva. Digital Beamforming in Wireless Communications. Artech House Publishers,

1996.[841] C.L. Liu and Jane W.S. Liu. Linear Systems Analysis. McGraw-Hill, New York, 1975.[842] Y.M. Liu. A distributional sampling theorem. SIAM Journal on Mathematical Analysis,

Vol. 27(4), pp. 1153–1157, 1996.[843] S.P. Lloyd. A sampling theorem for stationary (wide sense) stochastic processes. Transactions

America Math. Society, Vol. 92, pp. 1–12, 1959.[844] C. Loana, A. Quinquis, and Y. Stephan. Feature extraction from underwater signals using time-

frequency warping operators. IEEE Journal of Oceanic Engineering, Vol. 31(3), pp. 628–645,2006.

[845] Robert P. Loce and Ronald E. Jodoin. Sampling theorem for geometric moment determinationand its application to a laser beam position detector. Applied Optics, Vol. 29, No. 26,pp. 3835–3843, 1990.

[846] P.P. Loesberg. Low-frequency A-D input systems. Instrum. Control Syst., Vol. 43, pp. 124–126,1970.

[847] A.W. Lohmann and D.P. Paris. Binary Fraunhofer holograms, generated by computer. AppliedOptics, pp. 1739–1748, 1967.

[848] A.W. Lohmann. The space-bandwidth product applied to spatial filtering and to holography.IBM Research Paper, RJ-438, 1967.

[849] A.W. Lohmann and D.P. Paris. Computer generated spatial filters for coherent optical dataprocessing. Applied Optics, pp. 651–655, 1968.

[850] A.W. Lohmann. An interferometer based on the Talbot effect. Optical Communication,pp. 413–415, 1971.

[851] A.W. Lohmann. Three-dimensional properties of wave-fields. Optik, pp. 105–117, 1978.[852] P.J. Loughlin and G.D. Bernard. Cohen-Posch (positive) time-frequency distributions and

their application to machine vibration analysis. Mechanical Systems and Signal Processing.Vol. 11(4), pp. 561–576, 1997.

[853] P.J. Loughlin and K.L. Davidson. Modified Cohen-Lee time-frequency distributions andinstantaneous bandwidth of multicomponent signals. IEEE Transactions on Signal Processing,Vol. 49(6), pp. 1153–1165, 2001.

[854] D.G. Luenberger. Optimization by Vector Space Methods. Wiley, New York, 1969.[855] H.D. Luke. Zur Entsehung des Abtasttheorems. Nachr. Techn. Z., Vol. 31, pp. 271–274, 1978.


714 REFERENCES

[856] H.D. Luke. The origins of the sampling theorem IEEE Communications Magazine, Vol. 37(4),pp. 106–108, 1999.

[857] W. Lukosz. Optical systems with resolving powers exceeding the classical limit. Journal of theOptical Society America, Vol. 56, pp. 1463–1472, 1966.

[858] W. Lukosz. Optical systems with resolving powers exceeding the classical limit, II. Journal ofthe Optical Society America, Vol. 57, pp. 932–941, 1967.

[859] A. Luthra. Extension of Parseval’s relation to nonuniform sampling. IEEE Transactions Acoust.,Speech, Signal Processing, Vol. ASSP-36, No. 12, pp. 1909–1911, 1988.

M[860] Y.J. Ma and J.T. Sun. Stability criteria of delay impulsive systems on time scales. Nonlinear

Analysis–Theory Mathods & Applications, Vol. 67(4), pp. 1181–1189, 2007.[861] D.M. Mackay. Quantal aspects of scientific information. Phil. Mag., pp. 289–311, 1950.[862] D.M. Mackay. The structural information-capacity of optical instruments. Information &

Control, pp. 148–152, 1958.[863] J. Maeda and K. Murata. Digital restoration of incoherent bandlimited images. Applied Optics,

pp. 2199–2204, 1982.[864] H. Maitre. Iterative super-resolution. Some new fast methods. Opt. Acta, pp. 973–980, 1981.[865] Robert J. Mailloux. Phased Array Antenna Handbook, Second Edition. Artech House

Publishers; 2 edition, 2005.[866] J. Makhoul. Linear prediction: A tutorial review. Proceedings IEEE, Vol. 63, pp. 561–580,

1975.[867] T. Mallon. A Book of One’s Own. Ticknor & Fields, New York, 1984.[868] N.J. Malloy. Nonuniform sampling for high resolution spectrum analysis. In Proceedings

ICASSP’84, 1984.[869] L. Mandel and E. Wolf. Coherence properties of optical fields. Rev. Mod. Phys., pp. 231–287,

1965.[870] L. Mandel and E. Wolf. Spectral coherence and the concept of cross-spectral purity. Journal of

the Optical Society America, Vol. 66, pp. 529–535, 1976.[871] Thomas Mann. The Magic Mountain. Vintage; 1st Vintage International Edition, 1996.[872] M. Maqusi. A sampling theorem for dyadic stationary processes. IEEE Transactions Acoust.

Speech, Signal Processing, Vol. ASSP-26, pp. 265–267, 1978.[873] M. Maqusi. Truncation error bounds for sampling expansions of sequency band limited

signals. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-26, pp. 372–374,1978.

[874] M. Maqusi. Sampling representation of sequency bandlimited nonstationary random processes.IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-28, pp. 249–251, 1980.

[875] M. Maqusi. Correlation and spectral analysis of nonlinear transformation of sequencybandlimited signals. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-30,pp. 513–516, 1982.

[876] I. Maravic and M. Vetterli. Sampling and reconstruction of signals with finite rate of innovationin the presence of noise. IEEE Transactions on Signal Processing, Vol. 52(8), Part 1, pp. 2788–2805, 2005.

[877] E.W. Marchand and E. Wolf. Radiometry with sources of any state of coherence. Journal ofthe Optical Society America, Vol. 64, pp. 1219–1226, 1974.

[878] A. Maréchal and M. Françon. V Diffraction, structure des images. Masson, Paris, 1970.[879] H. Margenau and R.N. Hill. Correlation between measurements in quantum theory. Progress

in Theoretical Physics, Vol. 26, pp. 722–738, 1961.[880] C.P. Mariadassou and B. Yegnanarayana. Image reconstruction from noisy digital holograms.

IEE Proceedings F on Radar and Signal Processing, Vol. 137(5), pp. 351–356, 1990.[881] J.W. Mark and T.D. Todd. A nonuniform sampling approach to data compression. IEEE

Transactions Communications, Vol. COM-29, pp. 24–32, 1981.[882] W.D. Mark. Spectral analysis of the convolution and filtering of non-stationary stochastic

processes. Journal Sound Vib. Vol. 11, pp. 19–63, 1970.


REFERENCES 715

[883] J.D. Markel and H.H. Gray, Jr. Linear Prediction of Speech. Springer-Verlag, New York,1982.

[884] R.J. Marks II and T.F. Krile. Holographic representations of space-variant systems: Systemtheory. Applied Optics, Vol. 15, pp. 2241–2245, 1976.

[885] R.J. Marks II, J.F. Walkup, and M.O. Hagler. A sampling theorem for space-variant systems.Journal of the Optical Society America, Vol. 66, pp. 918–921, 1976.

[886] R.J. Marks II, J.F. Walkup, and T.F. Krile. Ambiguity function display: An improved coherentprocessor. Applied Optics Vol. 16, pp. 746–750, 1977.

[887] R.J. Marks II, J.F. Walkup, and M.O. Hagler. Line spread function notation. Applied Optics,Vol. 15, pp. 2289–2290, l976.

[888] R.J. Marks II, J.F. Walkup, and M.O. Hagler. Volume hologram representation of space-variant systems. In Applications of Holography and Optical Data Processing, E. Marom,A.A. Friesem, and E. Wiener-Aunear, editors, Oxford: Pergamon Press, pp. 105–113, 1977.

[889] R.J. Marks II, J.F. Walkup, and M.O. Hagler. Sampling theorems for linear shift-variant systems.IEEE Transactions Circuits & Systems, Vol. CAS-25, pp. 228–233, 1978.

[890] R.J. Marks II, G.L. Wise, D.G. Haldeman, and J.L. Whited. Detection in Laplace noise. IEEETransactions on Aerospace and Electronic Systems, Vol. AES-14, pp. 866–872, 1978.

[891] R.J. Marks II and J.N. Larson. One-dimensional Mellin transformation using a single opticalelement. Applied Optics, Vol. 18, pp. 754–755, 1979.

[892] R.J. Marks II. Two-dimensional coherent space-variant processing using temporal holography.Applied Optics, Vol. 18, pp. 3670–3674, 1979.

[893] R.J. Marks II, J.F. Walkup, and M.O. Hagler. Methods of linear system characterization throughresponse cataloging. Applied Optics, Vol. 18, pp. 655–659, 1979.

[894] R.J. Marks II and M.W. Hall. Ambiguity function display using a single 1-D input. in SPIEMilestone Series: Phase Space Optics, Markus Testorf, Jorge Ojeda-Castañeda, and AdolfLohmann, Editors, (The Society of Photo-Optical Instrumentation Engineers, Bellingham, WA,2006) reprinted from Applied Optics, Vol. 18(15), pp. 2539–2540, 1979.

[895] R.J. Marks II and D.K. Smith. An iterative coherent processor for bandlimited signalextrapolation. Proceedings of the 1980 International Computing Conference, Washington D.C.,1980.

[896] R.J. Marks II. Coherent optical extrapolation of two-dimensional signals: processor theory.Applied Optics, Vol. 19, pp. 1670–1672, 1980.

[897] R.J. Marks II. Gerchberg’s extrapolation algorithm in two dimensions. Applied Optics, Vol. 20,pp. 1815–1820, 1981.

[898] R.J. Marks II. Sampling theory for linear integral transforms. Opt. Letters, Vol. 6, pp. 7–9,1981.

[899] R.J. Marks II and M.J. Smith. Closed form object restoration from limited spatial and spectralinformation. Opt. Letters, Vol. 6, pp. 522–524, 1981.

[900] R.J. Marks II and M.W. Hall. Differintegral interpolation from a bandlimited signal’s samples.IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-29, pp. 872–877, 1981.

[901] R.J. Marks II. Posedness of a bandlimited image extension problem in tomography. Opt. Letters,Vol. 7, pp. 376–377, 1982.

[902] R.J. Marks II. Restoration of continuously sampled bandlimited signals from aliased data. IEEETransactions Acoust., Speech, Signal Processing, Vol. ASSP-30, pp. 937–942, 1982.

[903] R.J. Marks II and D. Kaplan. Stability of an algorithm to restore continuously sampledbandlimited images from aliased data. Journal of the Optical Society America, Vol. 73,pp. 1518–1522, 1983.

[904] R.J. Marks II. Noise sensitivity of bandlimited signal derivative interpolation. IEEETransactions Acoust., Speech, Signal Processing, Vol. ASSP-31, pp. 1029–1032, 1983.

[905] R.J. Marks II. Restoring lost samples from an oversampled bandlimited signal. IEEETransactions Acoust., Speech, Signal Processing, Vol. ASSP-31, pp. 752–755, 1983.

[906] R.J. Marks II and D. Radbel. Error in linear estimation of lost samples in an oversampledbandlimited signal. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-32,pp. 648–654, 1984.


716 REFERENCES

[907] R.J. Marks II and D.K. Smith. Gerchberg-type linear deconvolution and extrapolationalgorithms. In Transformations in Optical Signal Processing, W.T. Rhodes, J.R. Fienup,and B.E.A. Saleh, editors, Vol. 373, pp. 161–178, 1984.

[908] R.J. Marks II and S.M. Tseng. Effect of sampling on closed form bandlimited signal intervalinterpolation. Applied Optics, Vol. 24, pp. 763–765, Erratum, Vol. 24, p. 2490, 1985.

[909] R.J. Marks II. A class of continuous level associative memory neural nets. in SPIE MilestoneSeries: Selected Papers in Optical Neural Networks edited by Suganda Jutamulia (TheSociety of Photo-Optical Instrumentation Engineers, Bellingham, WA, 1994), pp. 331–336;reprinted from Applied Optics, Vol. 26, pp. 2005–2009, 1987.

[910] R.J. Marks II. Linear coherent optical removal of multiplicative periodic degradations:processor theory. Opt. Engineering, Vol. 23, pp. 745–747, 1984.

[911] R.J. Marks II. Multidimensional signal sample dependency at Nyquist densities. Journal of theOptical Society America A, Vol. 3, pp. 268–273, 1986.

[912] R.J. Marks II. Class of continuous level associative memory neural nets. Applied Optics,pp. 2005–2010, 1987.

[913] R.J. Marks II, S. Oh, and L.E. Atlas. Alternating projection neural networks. IEEE Transactionson Circuits and Systems, Vol. 36, pp. 846–857, 1989.

[914] R.J. Marks II, L.E. Atlas, and S. Oh. Optical neural net memory. U.S. Patent No. 4,849,940(assigned to the Washington Technology Center, University of Washington, Seattle), 1989.

[915] R.J. Marks II. Introduction to Shannon Sampling and Interpolation Theory. Springer-Verlag, New York, 1991.

[916] R.J. Marks II, Editor, Advanced Topics in Shannon Sampling and Interpolation Theory.Springer-Verlag, 1993.

[917] R.J. Marks II, Loren Laybourn, Shinhak Lee, and Seho Oh. Fuzzy and extra-crisp alternatingprojection onto convex sets (POCS). Proceedings of the International Conference on FuzzySystems (FUZZ-IEEE), Yokohama, Japan, pp. 427–435, 1995.

[918] R.J. Marks II, Alternating Projections onto Convex Sets, in Deconvolution of Images andSpectra, edited by Peter A. Jansson, (Academic Press, San Diego), pp. 476–501, 1997.

[919] R.J. Marks II. Method and Apparatus for Generating Sliding Tapered Windows and SlidingWindow Transforms. U.S. Patent No. 5,373,460, 1994.

[920] R.J. Marks II, B.B. Thompson, M.A. El-Sharkawi, W.L.J. Fox, and R.T. Miyamoto. Stochasticresonance of a threshold detector: image visualization and explanation. IEEE Symposium onCircuits and Systems, ISCAS, pp. IV-521–523, 2002.

[921] R.J. Marks II, Ian A. Gravagne, and John M. Davis, “A Generalized Fourier Transform andConvolution on Time Scales,” Journal of Mathematical Analysis and Applications, Vol. 340(2),pp. 901–919, 2008.

[922] R.J. Marks II, Ian Gravagne, John M. Davis, and Jeffrey J. DaCunha. Nonregressivity inswitched linear circuits and mechanical systems. Mathematical and Computer Modelling,Vol. 43, pp. 1383–1392, 2006.

[923] L. Marple, T. Brotherton, R. Barton, E. Lugo, and D. Jones. Travels through the time-frequencyzone: advanced Doppler ultrasound processing techniques. 1993 Conference Record of TheTwenty-Seventh Asilomar Conference on Signals, Systems and Computers, 1993. 1–3 Vol.2,pp. 1469–1473, 1993.

[924] M. Marques, A. Neves, J.S. Marques et al. The Papoulis-Gerchberg algorithm with unknownsignal bandwidth. Lecture Notes in Computer Science. 4141, pp. 436–445, 2006.

[925] Alan G. Marshall. Fourier, Hadamard, and Hilbert Transforms in Chemistry. PerseusPublishing, 1982.

[926] A.G. Marshall and F.R. Verdun. Fourier transforms in NMR, Optical and MassSpectrometry. Elsevier, Amsterdam, 1990.

[927] R.J. Martin. Volterra system identification and Kramer’s sampling theorem. IEEE Transactionson Signal Processing, Vol. 47(11), pp. 3152–3155, 1999.

[928] H.G. Martinez and T.W. Parks. A class of infinite-duration impulse response digital filters forsampling rate reduction. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-27,pp. 154–162, 1979.


REFERENCES 717

[929] S.A. Martucci. Symmetric convolution and the discrete sine and cosine transforms. IEEETransactions Sig. Processing, SP–42, 1038–1051 1994.

[930] F. Marvasti. The extension of Poisson sum formula to nonuniform samples. Proceedings 5thAachener Kolloquium, Aachen, Germany, 1984.

[931] F. Marvasti. A note on modulation methods related to sine wave crossings. IEEE TransactionsCommunications, pp. 177–178, 1985.

[932] F. Marvasti. Reconstruction of a signal from the zero-crossings of an FM signal. TransactionsIECE of Japan, p. 650, 1985.

[933] F. Marvasti. Signal recovery from nonuniform samples and spectral analysis of random samples.In IEEE Proceedings on ICASSP, Tokyo, pp. 1649–1652, 1986.

[934] F. Marvasti. Spectral analysis of random sampling and error free recovery by an iterativemethod. IECE Transactions of Institute Electron. Commun. Engs., Japan (Section E), Vol. E 69,No. 2, 1986.

[935] F. Marvasti. A unified approach to zero-crossings, nonuniform and random sampling of signalsand systems. In Proceedings of the International Symposium on Signal Processing and ItsApplications, Brisbane, Australia, pp. 93–97, 1987.

[936] F. Marvasti. Minisymposium on zero-crossings and nonuniform sampling, In Abstract of 4presentations in the Proceedings of SIAM Annual Meeting, Minneapolis, Minnesota, 1988.

[937] F. Marvasti. Analysis and recovery of sample-and-hold signals with irregular samples. InAnnual Proceedings of the Allerton Conference on Communication, Control and Computing,1989.

[938] F. Marvasti. Minisymposium on nonuniform sampling for 2-D signals. In Abstract of 4presentations in the Proceedings of SIAM Annual Meeting, San Diego, California, 1989.

[939] F. Marvasti. Rebuttal on the comment on the properties of two-dimensional bandlimited signals.Journal of the Optical Society America A, Vol. 6, No. 9, p. 1310, 1989.

[940] F. Marvasti. Reconstruction of 2-D signals from nonuniform samples or partial information.Journal of the Optical Society America A, Vol. 6, pp. 52–55, 1989.

[941] F. Marvasti. Relationship between discrete spectrum of frequency modulated (FM) signals andalmost periodic modulating signals. Transactions IECE Japan, pp. 92–94, 1989.

[942] F. Marvasti. Spectral analysis of nonuniform samples of irregular samples of multidimensionalsignals. In 6th Workshop on Multidimensional Signal Processing, California, 1989.

[943] F. Marvasti. Extension of Lagrange interpolation to 2-D signals in polar coordinates. IEEETransactions Circuits & Systems, 1990.

[944] F. Marvasti. The interpolation of 2-D signals from their isolated zeros. JournalMultidimensional Systems and Signal Processing, 1990.

[945] F. Marvasti and M. Analoui. Recovery of signals from nonuniform samples using iterativemethods. In IEEE Proceedings of International Conference on Circuits and Systems, Oregon,1989.

[946] F. Marvasti, M. Analoui, and M. Gamshadzahi. Recovery of signals from nonuniform samplesusing iterative methods. IEEE Transactions Acoust., Speech, Signal Processing, 1991.

[947] F. Marvasti, Peter Clarkson, Dobcik Miraslov, and Chuande Liu. Speech recovery from missingsamples. In Proceedings IASTED Conference on Control and Modeling, Tehran, Iran, 1990.

[948] F. Marvasti and Reda Siereg. Digital signal processing using FM zero-crossing. In Proceedingsof IEEE International Conference on Systems Engineering, Wright State University, 1989.

[949] F.A. Marvasti. Spectrum of nonuniform samples. Electron. Letters, Vol. 20, No. 2, 1984.[950] F.A. Marvasti. Comments on a note on the predictability of bandlimited processes. Proceedings

IEEE, Vol. 74, p. 1596, 1986.[951] F.A. Marvasti. A Unified Approach to Zero-Crossing and Nonuniform Sampling of Single and

Multidimensional Signals and Systems. Nonuniform Publications, Oak Park, IL, 1987.[952] F.A. Marvasti and A.K. Jain. Zero crossings, bandwidth compression and restoration of

nonlinearly distorted bandlimited signals. Journal of the Optical Society America A, Vol. 3,pp. 651–654, 1986.

[953] F.A. Marvasti. Extension of Lagrange interpolation to 2-D nonuniform samples in polarcoordinates. IEEE Transactions Circuits & Systems, Vol. 37, No. 4, pp. 567–568, 1990.


718 REFERENCES

[954] F.A. Marvasti and Liu Chuande. Parseval relationship of nonuniform samples of one and two-dimensional signals. IEEE Transactions Acoust., Speech, Signal Processing, Vol. 38, No. 6,pp. 1061–1063, 1990.

[955] F.A. Marvasti. Oversampling as an alternative to error correction codes. Minisymposium onSampling Theory and Practice, SIAM Annual Meeting, Chicago, IL, July 1990. Also in ICC’92,Chicago, IL, 1992.

[956] F.A. Marvasti and T.J. Lee. Analysis and recovery of sample-and -hold and linearlyinterpolated signals with irregular samples. IEEE Transactions Signal Processing, Vol. 40,No. 8, pp. 1884–1891, 1992.

[957] FarokhA. Marvasti. Nonuniform Sampling:Theory and Practice (InformationTechnology:Transmission, Processing, and Storage). Kluwer Academic/Plenum Publishers, 2001.

[958] E. Masry. Random sampling and reconstruction of spectra. Inf. Contr., Vol. 19, pp. 275–288,1971.

[959] E. Masry. Alias-free sampling: an alternative conceptualization and its applications. IEEETransactions Information Theory, Vol. IT–24, 1978.

[960] E. Masry. Poisson sampling and spectral estimation of continuous time processes. IEEETransactions Information Theory, Vol. IT–24, 1978.

[961] E. Masry. The reconstruction of analog signals from the sign of their noisy samples. IEEETransactions Information Theory, Vol. IT–27, pp. 735–745, 1981.

[962] E. Masry. The approximation of random reference sequences to the reconstruction of clippeddifferentiable signals. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-30,pp. 953–963, 1982.

[963] E. Masry and S. Cambanis. Bandlimited processes and certain nonlinear transformations.Journal Math. Anal., Vol. 53, pp. 59–77, 1976.

[964] E. Masry and S. Cambanis. Consistent estimation of continuous time signals from nonlineartransformations of noisy samples. IEEE Transactions Information Theory, Vol. IT–27,pp. 84–96, 1981.

[965] E. Masry, D. Kramer, and C. Mirabile. Spectral estimation of continuous time process:performance comparison between periodic and Poisson sampling schemes. IEEE TransactionsAutomatic Control, Vol. AC-23, pp. 679–685, 1978.

[966] Georges Matheron, Random Sets and Integral Geometry, John Wiley & Sons, New York,1975.

[967] J. Mathews and R.L. Walker. Mathematical Methods of Physics, 2nd ed. W.A. Benjamin,Menlo Park, CA, 1970.

[968] D. Maurice. Convolution and Fourier Transforms for Communications Engineers. JohnWiley & Sons, 1976.

[969] A.C. McBride and F.H. Kerr. On Namias’s fractional Fourier transform. IMA J. Applied Math.,Vol. 39, pp. 159—175, 1987.

[970] James H. McClellan. The Design of Two Dimensional Filters by Transformation. Proceedings7th Annual Princeton Conference on Information Sciences and Systems, pp. 247–251, 1973.

[971] James H. McClellan and David S.K. Chan. A 2-D FIR Filter Structure Derived fromthe Chebyshev Recursion. IEEE Transactions on Circuits and Systems, CAS–24, No. 7,pp. 372–378, 1977.

[972] M.J. McDonnell. A sampling function appropriate for deconnotation. IEEE TransactionsInformation Theory, Vol. IT-22, pp. 617–621, 1976.

[973] K.C. McGill and L.J. Dorfman. High-resolution alignment of sampled waveforms. IEEETransactions Biomedical Engineering, Vol. BME–31, pp. 462–468, 1984.

[974] J. McNamee, F. Stenger, and E.L. Whitney. Whittaker’s cardinal function in retrospect. Math.Comp. Vol. 25, pp. 141–154, 1971.

[975] A.K. Menon and Z.E. Boutaghou. Time-frequency analysis of tribological systems – part I:implementation and interpretation. Tribiological International. Vol. 31(9), pp. 501–510, 1998.

[976] W.F.G. Mechlenbräuker, Russell M. Mersereau, McClellan Transformation for 2-D DigitalFiltering: I-Implementation. IEEE Transactions on Circuits and Systems, CAS-23, No. 7,pp. 414–422, 1976.


REFERENCES 719

[977] Alfred Mertins. SignalAnalysis: Wavelets, Filter Banks, Time-Frequency Transforms andApplications. Wiley, 1999.

[978] F.C. Mehta. A general sampling expansion. Inform. Sci., Vol. 16, pp. 41–44, 1978.[979] P.M. Mejías and R. Martínez Herrero. Diffraction by one-dimensional Ronchi grids: on the

validity of the Talbot effect. Journal of the Optical Society America A, Vol. 8, pp. 266–269,1991.

[980] Russell M. Mersereau, W.F.G. Mechlenbräuker, and T.F. Quatieri. McClellan Transformationfor 2-D Digital Filtering: I-Design. IEEE Transactions on Circuits and Systems, CAS-23,No. 7, pp. 405–414, 1976.

[981] R.M. Mersereau. The processing of hexagonally sampled two dimensional signals.Proceedings IEEE, Vol. 67, pp. 930–949, 1979.

[982] R.M. Mersereau and T.C. Speake. The processing of periodically sampled multidimensionalsignals. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-31, No. 31,pp. 188–194, 1983.

[983] D. Middleton. An Introduction to Statistical Communication Theory. McGraw-Hill,New York, 1960.

[984] D. Middleton and D.P. Peterson. A note on optimum presampling filters. IEEE TransactionsCircuit Theory, Vol. CT-10, pp. 108–109, 1963.

[985] J. Millet-Roig, J.J. Rieta-Ibanez, E. Vilanova, A. Mocholi, and F.J. Chorro. Time-frequencyanalysis of a single ECG: to discriminate between ventricular tachycardia and ventricularfibrillation. Computers in Cardiology 1999, 26–29 pp. 711–714, 1999.

[986] R. Mintzer and B. Liu. Aliasing error in the design of multirate filters. IEEE TransactionsAcoust., Speech, Signal Processing, Vol. ASSP-26, pp. 76–88, 1978.

[987] R. Mirman. Point Groups, Space Groups, Crystals, Molecules. World Scientific, 1999.[988] S. Mitaim and B. Kosko. Adaptive stochastic resonance. Proceedings of the IEEE. Vol. 86,

No. 11, 1998.[989] J.R. Mitchell and W.L. McDaniel Jr. Adaptive sampling technique. IEEE Transactions

Automatic Control, Vol. AC-14, pp. 200–201, 1969.[990] J.R. Mitchell and W.L. McDaniel Jr. Calculation of upper bounds for errors of an approximate

sampled frequency response. IEEE Transactions Automatic Control, Vol. AC-19, pp. 155–156,1974.

[991] Sanjit K. Mitra. Digital Signal Processing, McGraw-Hill Science/Engineering/Math; 3rdedition 2005.

[992] H. Miyakawa. Sampling theorem of stationary stochastic variables in multi-dimensional space(Japanese). Journal Institute Electron. Commun. Engineering Japan, Vol. 42, pp. 421–427,1959.

[993] K. Miyamoto. On Gabor’s expansion theorem. Journal of the Optical Society America, Vol. 50,pp. 856–858, 1960.

[994] K. Miyamoto. Note on the proof of Gabor’s expansion theorem. Journal of the Optical SocietyAmerica, Vol. 51, pp. 910–911, 1961.

[995] W.D. Montgomery. The gradient in the sampling of n-dimensional bandlimited functions.Journal Electron. Contr., Vol. 17, pp. 437–447, 1964.

[996] W.D. Montgomery. Algebraic formulation of diffraction applied to self-imaging. Journal ofthe Optical Society America, Vol. 58, pp. 1112–1124, 1968.

[997] D.R. Mook, G.V. Fisk, and A.V. Oppenheim. A hybrid numerical-analytical technique forthe computation of wave fields in stratified media based on the Hankel transform. JournalAcoustics. Society America, Vol. 76, No. 1, pp. 222–243, 1984.

[998] N. Moray, G. Synnock, and S. Richards. Tracking a static display. IEEE Transactions Systems,Man, Cybernetics, Vol. SMC-3, pp. 518–521, 1973.

[999] Frank Morgan. RealAnalysis andApplications: Including Fourier Series and the Calculusof Variations. American Mathematical Society, 2005.

[1000] F. Mori and J. De Steffano III. Optimal nonuniform sampling interval and test-input design foridentification of physiological systems from very limited data. IEEE Transactions AutomaticControl, Vol. AC-24, No. 6, pp. 893–900, 1979.


720 REFERENCES

[1001] H. Mori, I. Oppenheim, and J. Ross. Some Topics in Quantum Statistics: The Wigner Functionand Transport Theory. In Studies in Statistical Mechanics, J. de Boer and G.E. Uhlenbeck,eds. North-Holland, Amsterdam, Vol. 1, pp. 213–298, 1962.

[1002] Norman Morrison. Introduction to Fourier Analysis. Wiley-Interscience, 1995.[1003] G.V. Moustakides and E.Z. Psarakis. Design of N-dimensional hyperquadrantally symmetric

FIR filters using the McClellan transform. IEEE Transactions on Circuits and Systems II:Analog and Digital Signal Processing, Vol. 42(8), pp. 547–550, 1995.

[1004] K. Mullen and PS. Pregosin. Fourier Transform Nuclear Magnetic Resonance Techniques.Academic Press, 1977.

[1005] D.H. Mugler and W. Splettstößer. Difference methods and round-off error bounds for theprediction of bandlimited-functions from past samples. Frequenz, Vol. 39, pp. 182–187, 1985.

[1006] D.H. Mugler and W. Splettstößer. Some new difference schemes for the prediction ofbandlimited signals from past samples. In Proceedings of the Conference “Mathematics inSignal Processing” Bath, 1985.

[1007] D.H. Mugler and W. Splettstößer. Difference methods for the prediction of bandlimited signals.SIAM Journal Applied Math., Vol. 46, pp. 930–941, 1986.

[1008] H.D. Mugler and W. Splettstößer. Linear prediction from samples of a function and itsderivatives. IEEE Transactions Information Theory, Vol. IT–33, pp. 360–366, 1987.

[1009] K. Mullen, P.S. Pregosin. Fourier Transform Nuclear Magnetic Resonance Techniques:A Practical Approach. Elsevier Science & Technology Books, 1977.

[1010] N.J. Munch. A Twisted Sampling Theorem. IMA Journal of Mathematical Control andInformation, Vol. 7(1), pp. 47–57, 1990.

[1011] D.C. Munson. Minimum sampling rates for linear shift-variant discrete-time systems. IEEETransactions Acoust., Speech, Signal Processing, Vol. ASSP–33, pp. 1556–1561, 1985.

[1012] P.K. Murphy and N.C. Gallagher.Anew approach to two-dimensional phase retrieval. Journalof the Optical Society America, Vol. 72, pp. 929–937, 1982.

N[1013] T. Nagai. Dyadic stationary processes and their spectral representation. Bull. Math. Stat.,

Vol. 17, pp. 65–73, 1976/77.[1014] N. Nakajima and T. Asakura. A new approach to two-dimensional phase retrieval. Opt. Acta,

Vol. 32, pp. 647–658, 1985.[1015] V. Namias. The fractional order Fourier transform and its applications to quantum mechanics.

J. Institute Math. Applied, Vol. 25, pp. 241–265, 1980.[1016] H. Nassenstein. Super-resolution by diffraction of subwaves. Optical Communication,

pp. 231–234, 1970.[1017] A. Nathan. On sampling a function and its derivatives. Information & Control, Vol. 22,

pp. 172–182, 1973.[1018] A. Nathan. Plain and covariant multivariate Fourier transforms. Information & Control,Vol. 39,

pp. 73–81, 1978.[1019] J.L. Navarro-Mesa, E. Lleida-Solano, and A.A. Moreno-Bilbao. A new method for epoch

detection based on the Cohen’s class of time frequency representations. IEEE SignalProcessing Letters, Vol. 8(8), pp. 225–227, 2001.

[1020] A.W. Naylor and G.R. Sell. Linear Operator Theory in Engineering and Science. Springer-Verlag, New York, 1982.

[1021] S.A. Neild, P.D. McFadden, and M.S. Williams. A review of time-frequency methods forstructural vibration analysis. Engineering Structures, Vol. 5(6), pp. 713–728, 2003.

[1022] Kazuki Nishi. Generalized comb function: a new self-Fourier function. IEEE InternationalConference on Acoustics, Speech, and Signal Processing, 2004. (ICASSP ’04). Vol. 2,pp. 573–576.

[1023] J. Ojeda-Castañeda, J. Ibarra, and J.C. Barreiro. Noncoherent Talbot effect: Coherence theoryand applications. Optical Communication, Vol. 71, pp. 151–155, 1989.

[1024] J. Ojeda-Castañeda and E.E. Sicre. Quasi ray-optical approach to longitudinal periodicitiesof free and bounded wavefields. Opt. Acta, pp. 17–26, 1985.


REFERENCES 721

[1025] J. Von Neumann. The Geometry of Orthogonal Spaces. Princeton University Press,Princeton, New Jersey, 1950.

[1026] J. Von Neumann. Mathematical Foundations of Quantum Mechanics. Princeton UniversityPress, 1955, Chap. 5, Sect. 4.

[1027] B. Nicoletti and L. Mariani. Optimization of nonuniformly sampled discrete systems.Automatica, Vol. 7, pp. 747–753, 1971.

[1028] K. Niederdrenk. The Finite Fourier and Walsh Transformation with an Introduction toImage Processing. Vieweg & Sohn, Braunschweig, 1982.

[1029] Y. Noguchi, E. Kashiwagi, E. Kashiwagi et al. Ultrasound Doppler sinusoidal shift signalanalysis by time-frequency distribution with new kernel. Japanese Journal of Applied PhysicsPart 1, Vol. 37(5B), pp. 3064–3067, Sp. Iss. SI 1998.

[1030] Y. Noguchi, E. Kashiwagi, K. Watanabe et al. Time-frequency analysis of the bloodflow Doppler ultrasound signal. Japanese Journal of Applied Physics Part 1, Vol. 40(5B),pp. 3882–3887, 2001.

[1031] Stephen Abbott Northrop. A Cloud of Witnesses. (Portland, Oregon: American HeritageMinistries, 1987; Mantle Ministries, 228 Still Ridge, BuIverde, Texas), pp. 147–8.

[1032] K.A. Nugent. Three-dimensional optical microscopy: a sampling theorem. OpticalCommunication, pp. 231–234, 1988.

[1033] H. Nyquist. Certain topics in telegraph transmission theory. AIEE Transactions, Vol. 47,pp. 617–644, 1928.

[1034] D. Nguyen and M. Swamy. Formulas for parameter scaling in the McClellan transform. IEEETransactions on Circuits and Systems, Vol.33(1), pp. 108–109, 1986.

[1035] D. Nguyen and M. Swamy. A class of 2-D separable denominator filters designed via theMcClellan transform. IEEE Transactions on Circuits and Systems, Vol. 33(9), pp. 874–881,1986.

O[1036] K. Ogura. On a certain transcendental integral function in the theory of interpolation. Tôhoku

Math. J., Vol. 17, pp. 64–72, 1920.[1037] S. Oh, R.J. Marks II, L.E. Atlas and J.W. Pitton. Kernel synthesis for generalized time-

frequency distributions using the method of projection onto convex sets. SPIE Proceedings1348, Advanced Signal Processing Algorithms, Architectures, and Implementation,F.T. Luk, Editor, San Diego, pp. 197–207, 1990.

[1038] S. Oh and R.J. Marks II. Performance attributes of generalized time-frequency representationswith double diamond and cone shaped kernels. Proceedings of the Twenty Fourth AsimomarConference on Signals, Systems and Computers, 5–7 November, 1990, Asilomar ConferenceGrounds, Monterey, California.

[1039] S. Oh, R.J. Marks II, and Dennis Sarr. Homogeneous alternating projection neural networks.Neurocomputing, Vol. 3, pp. 69–95, 1991.

[1040] S. Oh, C.Ramon, M.G. Meyer, A. C. Nelson, and R.J. Marks II. Resolution enhancementof biomagnetic images using the method of alternating projections. IEEE Transactions onBiomedical Engineering, Vol. 40, No. 4, pp. 323–328, 1993.

[1041] S. Oh and R.J. Marks II. Alternating projections onto fuzzy convex sets. Proceedings of theSecond IEEE International Conference on Fuzzy Systems, (FUZZ-IEEE ‘93), San Francisco,Vol.1, pp. 148–155, 1993.

[1042] S. Oh and R.J. Marks II. Some properties of the generalized time frequency representation withcone shaped kernels. IEEE Transactions on Signal Processing, Vol.40, No.7, pp. 1735–1745,1992.

[1043] S. Oh, R.J. Marks II, and L.E. Atlas. Kernel synthesis for generalized time-frequencydistributions using the method of alternating projections onto convex sets. IEEE Transactionson Signal Processing, Vol. 42, No.7, pp. 1653–1661, 1994.

[1044] N. Ohyama, M. Yamaguchi, J. Tsujiuchi, T. Honda, and S. Hiratsuka. Suppression of Moiréfringes due to sampling of halftone screened images. Optical Communication, pp. 364–368,1986.


722 REFERENCES

[1045] K.B. Oldham and J. Spanier. The Fractional Calculus. Academic Press, New York, 1974.[1046] A.Y. Olenko and T.K. Pogany. Time shifted aliasing error upper bounds for truncated sampling

cardinal series. Journal of Mathematical Analysis and Applications, Vol. 324(1), pp. 262–280,2006.

[1047] B.L. Ooi, S. Kooi, and Leong M.S. Application of Sonie-Schafheitlin formula andsampling theorem in spectral-domain method. IEEE Transactions on Microwave Theory andTechniques, 49(1), pp. 210–213, 2001.

[1048] E.L. O’Neill. Spatial filtering in optics. IRE Transactions Information Theory, pp. 56–62,1956.

[1049] E.L. O’Neill. Introduction to Statistical Optics. Addison-Wesley, Reading, MA, 1963.[1050] E.L. O’Neill and A. Walther. The question of phase in image formation. Opt. Acta, pp. 33–40,

1962.[1051] L. Onural. Exact analysis of the effects of sampling of the scalar diffraction field. Journal of

the Optical Society of America A – Optics, Image Science and Vision, Vol. 24(2), pp. 359–367,2007.

[1052] Z. Opial. Weak convergence of the sequence of successive approximation for nonexpansivemappings. Bull. Amer. Math. Society, Vol. 73, pp. 591–597, 1967.

[1053] A.V. Oppenheim and R.W. Shafer. Digital Signal Processing. Prentice-Hall, EnglewoodCliffs, NJ, 1975 - updated in [1054].

[1054] A.V. Oppenheim, R.W. Schafer, and J.R. Buck, Discrete-Time Signal Processing, secondedition (Prentice-Hall, New Jersey, 1999)–an updated version of [1053].

[1055] A.V. Oppenheim. Digital processing of speech. In Applications of Digital Signal Processing.Prentice-Hall, Englewood Cliffs, NJ, 1978.

[1056] A.V. Oppenheim, Alan, S. Willsky, and Ian T. Young. Signals and Systems. Prentice-Hall,Englewood Cliffs, NJ, 1983.

[1057] J.F. Ormsky. Generalized interpolation sampling expressions and their relationship. JournalFranklin Institute, Vol. 310, pp. 247–257, 1980.

[1058] L. Stankovic, T. Alieva, and M.J. Bastiaans. Time-frequency signal analysis based on thewindowed fractional Fourier transform. Signal Processing, Vol. 83(11), pp. 2459–2468, 2003.

[1059] Radomir S. Stankovic, Claudio Moraga, and Jaakko Astola. Fourier Analysis on FiniteGroups with Applications in Signal Processing and System Design. Wiley-IEEE Press,2005.

[1060] P. Oskoui-Fard, H. Stark. Geometry-free X-ray reconstruction using the theory of convexprojections 1988 International Conference on Acoustics, Speech, and Signal Processing,ICASSP–88., pp. 871–874, 1988.

[1061] T.J. Osler. A further extension of the Leibnitz rule for fractional derivatives and its relation toParseval’s formula. SIAM J. Math. Anal., Vol. 4, No. 4, 1973.

[1062] L.E. Ostrander. The Fourier transform of spline function approximations to continuous data.IEEE Transactions Audio Electroacoustics., Vol. AU-19, pp. 103–104, 1971.

[1063] J.S. Ostrem. A sampling series representation of the gain and refractive index formulas fora combined homogeneously and inhomogeneously broadened laser line. Proceedings IEEE,Vol. 66, pp. 583–589, 1978.

[1064] N. Ostrowsky, D. Sornette, P. Parker, and E.R. Pike. Exponential sampling method for lightscattering polydispersity analysis. Opt. Acta, Vol. 28, pp. 1059–1070, 1981.

[1065] M.K. Ozkan, A.M. Tekalp, and M.I. Sezan. POCS-based restoration of space-varying blurredimages. IEEE Transactions on Image Processing, Vol. 3(4), pp. 450–454, 1994.

[1066] H.M. Ozaktas, O. Arikan, M.A. Kutay, and G. Bozdagt. Digital computation of the fractionalFourier transform. IEEE Transactions on Signal Processing, Vol. 44(9), pp. 2141–2150,1996.

[1067] H.M. Ozaktas, N. Erkaya, and M.A. Kutay. Effect of fractional Fourier transformation ontime-frequency distributions belonging to the Cohen class. IEEE Signal Processing Letters,Vol. 3(2), pp. 40–41, 1996.

[1068] Haldun M. Ozaktas, Zeev Zalevsky, and M. Alper. The Fractional Fourier Transform: withApplications in Optics and Signal Processing, John Wiley & Sons, 2001.


REFERENCES 723

P[1069] Hoon Paek, Rin-Chul Kim, and Sang-Uk Lee. On the POCS-based postprocessing technique

to reduce the blocking artifacts in transform coded images. IEEE Transactions on Circuitsand Systems for Video Technology, Vol. 8(3), pp. 358–367, 1998.

[1070] C.H. Page. Instantaneous Power Spectra. Jour. Applied Phy., Vol.23, pp. 103–106, 1952.[1071] R.E.A. Paley and N. Wiener. Fourier Transform in Complex Domain. Colloq. Publications,

American Math. Society, New York, Vol. 19, 1934.[1072] F. Palmieri. Sampling theorem for polynomial interpolation. IEEE Transactions Acoust.,

Speech, Signal Processing, Vol. ASSP-34, pp. 846–857, 1986.[1073] T. Pappas. Mersenne’s Number. The Joy of Mathematics. San Carlos, CA: Wide World Publ.

Tetra, P. 211, 1989.[1074] A. Papoulis. The Fourier Integral and Its Applications. McGraw-Hill, New York, 1962.[1075] A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, NY,

1965.[1076] A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed., McGraw-

Hill, NY, 1984.[1077] A. Papoulis. Probability, Random Variables, and Stochastic Processes, 3rd ed. McGraw-

Hill, New York, 1991.[1078] Papoulis and S.Unnikrishna Pillai. Probability, Random Variables and Stochastic

Processes. 4th Revised Edition, McGraw Hill, 2002.[1079] A. Papoulis. Error analysis in sampling theory. Proceedings IEEE, Vol. 54, pp. 947–955,

1966.[1080] A. Papoulis. Limits on bandlimited signals. Proceedings IEEE, Vol. 55, pp. 1677–1681, 1967.[1081] A. Papoulis. Truncated sampling expansions. IEEE Transactions Automatic Control,

pp. 604–605, 1967.[1082] A. Papoulis. Systems and Transforms with Applications in Optics. McGraw-Hill,

New York, 1968.[1083] A. Papoulis and M.S. Bertran. Digital filtering and prolate functions. IEEE Transactions

Circuits & Systems, Vol. CT-19, pp. 674–681, 1972.[1084] A. Papoulis. A new method of image restoration. Joint Services Technical Activity Report, 39,

1973–74.[1085] A. Papoulis. A new algorithm in spectral analysis and bandlimited signal extrapolation. IEEE

Transactions Circuits & Systems, Vol. CAS-22, pp. 735–742, 1975.[1086] A. Papoulis. Generalized sampling expansion. IEEE Transactions Circuits & Systems,

Vol. CAS–24, pp. 652–654, 1977.[1087] A. Papoulis. Signal Analysis. McGraw-Hill, New York, 1977.[1088] A. Papoulis. Circuits and Systems, A Modern Approach. Holt, Rinehart and Winston, Inc.,

New York, 1980.[1089] A. Papoulis. A note on the predictability of bandlimited processes. Proceedings IEEE, Vol. 73,

pp. 1332–1333, 1985.[1090] G.Y. Park, C.K. Lee, J.T. Kim, K.C. Kwon, and S.J. Lee. Design of a time-frequency

distribution for vibration monitoring under corrosions in the pipe. Proceedings KeyEngineering Materials for Advanced Nondestructive Evaluations. pp. 321–323, 1257–1261,2006.

[1091] Jiho Park, D.C. Park, R.J. Marks II, and M.A. El-Sharkawi. Block loss recovery in DCT imageencoding using POCS. IEEE International Symposium on Circuits and Systems, Scottsdale,Arizona, pp. V245–V248, 2002.

[1092] Jiho Park, R.J. Marks II, D.C. Park, and M.A. El-Sharkawi. Content based adaptive spatio-temporal methods for MPEG repair. IEEE Transactions on Image Processing, Vol. 13, # 8,pp. 1066–1077, 2004.

[1093] Jiho Park, Dong Chul Park, R.J. Marks II, and M.A. El-Sharkawi. Recovery of image blocksusing the method of alternating projections. IEEE Transactions on Image Processing, 2005.

[1094] J.B. Park and D.G. Nishimura, Effects of 3D sampling in (k,t)-space on temporal qualities ofdynamic MRI . Magnetic Resonance Imaging, Vol. 24(8), pp. 1009–1014, 2006.


724 REFERENCES

[1095] T.W. Parks and R.G. Meier. Reconstructions of signals of a known class from a givenset of linear measurements. IEEE Transactions Information Theory, Vol. IT–17, pp. 37–44,1971.

[1096] E. Parzen. A simple proof and some extensions of sampling theorems. Technical report,Stanford University, Stanford, California, 1956.

[1097] E. Parzen. Stochastic Processes. Holden-Day, San Francisco, 1962.[1098] Blaise Pascal, translated by A. J. Krailsheimer. Pensées. Penguin Classics; Reissue edition,

1995.[1099] C. Pask. Simple optical theory of optical super-resolution. Journal of the Optical Society

America, Vol. 66, pp. 68–69a, 1976.[1100] K. Patorski. The self-imaging phenomenon and its applications. In Progress in Optics, North-

Holland, Amsterdam, 1989.[1101] Soo-Chang Pei, Min-Hung Yeh, and Tzyy-Liang Luo. Fractional Fourier series expansion

for finite signals and dual extension to discrete-time fractional Fourier transform. IEEETransactions on Signal Processing, Vol. 47(10), pp. 2883–2888, 1999.

[1102] Soo-Chang Pei, Min-HungYeh, and Chien-Cheng Tseng. Discrete fractional Fourier transformbased on orthogonal projections. IEEE Transactions on Signal Processing, Vol. 47(5),pp. 1335–1348, 1999.

[1103] Haidong Peng, Mohammad Sabati, Louis Lauzon, and Richard Frayne. MR imagereconstruction of sparsely sampled 3D k-space data by projection-onto-convex sets. MagneticResonance, Vol. 24(6), pp. 761–773, 2006.

[1104] Hui Peng and Henry Stark. Signal recovery with similarity constraints. Journal of the OpticalSociety of America A, Vol 6, No.6, pp. 844–851, 1989.

[1105] L.M. Peng. Sampling theorem and digital electron microscopy. Progress in Natural Science,Vol. 7(1), pp. 110–114, 1997.

[1106] L.E. Pellon. A double Nyquist digital product detector for quadrature sampling. IEEETransactions Signal Processing, Vol. 40, pp. 1670–1681, 1992.

[1107] I. Pesenson. A sampling theorem on homogeneous manifolds. Transactions of the AmericanMathematical Society, Vol. 352(9), pp. 4257–4269, 2000.

[1108] R.J. Peterka, D.P. Oleary, and A.C. Sanderson. Practical considerations in the implementationof the French-Holden algorithm for sampling of neuronal spike trains. IEEE TransactionsBiomedical Engineering, Vol. BME-24, pp. 192–195, 1978.

[1109] Terry M. Peters, J. C. Williams, and J. H. Bates, (Editors). Fourier Transform in BiomedicalEngineering Birkhauser Verlag, 1997.

[1110] D. P. Petersen. Sampling of space-time stochastic processes with application to informationand design systems, Thesis, Rensselaer Polytechnic Inst., Troy, N. Y. 1963.

[1111] D.P. Petersen. Discrete and fast Fourier transformations on n-dimensional lattices.Proceedings IEEE, Vol. 58, 1970.

[1112] D.P. Petersen and D. Middleton. Sampling and reconstruction of wave number-limitedfunction in n-dimensional Euclidean spaces. Inform., Contr., Vol. 5, pp. 279–323, 1962.

[1113] D.P. Petersen and D. Middleton. Reconstruction of multidimensional stochastic fields fromdiscrete measurements of amplitude and gradient. Information & Control, Vol. 1, pp. 445–476,1964.

[1114] D.P. Petersen and D. Middleton. Linear interpolation, extrapolation and prediction of randomspace-time fields with limited domain of measurement. IEEE Transactions InformationTheory, Vol. IT–11, 1965.

[1115] J. Perina. Holographic method of deconvolution and analytic continuation. CzechoslovakJ. Phys., Vol. B21, pp. 731–748, 1971.

[1116] J. Perina and J. Kvapil. A note on holographic method of deconvolution. Optik, pp. 575–577,1968.

[1117] J. Perina, V. Perinova, and Z. Braunerova. Super-resolution in linear systems with noise.Optica Applicata, pp. 79–83, 1977.

[1118] E.P. Pfaffelhuber. Sampling series for bandlimited generalized functions. IEEE TransactionsInformation Theory, Vol. IT-17, pp. 650–654, 1971.


REFERENCES 725

[1119] F. Pichler. Synthese linearer periodisch zeitvariabler Filter mit vorgeschriebenem Sequen-zverhalten. Arch. Elek. Übertr. (AEÜ), Vol. 22, pp. 150–161, 1968.

[1120] W.J. Pielemeier and G.H. Wakefield. A high-resolution time-frequency representation formusical instrument signals. Journal of the Acoustical Society of America. Vol. 99(4),pp. 2382–2396, 1996.

[1121] W.J. Pielemeier, G.H. Wakefield, and M.H. Simoni. Time-frequency analysis of musicalsignals. Proceedings of the IEEE. Vol. 84(9), pp. 1216–1230, 1996.

[1122] Allan Pinkus and Samy Zafrany. Fourier Series and Integral Transforms. CambridgeUniversity Press, 1997.

[1123] H.S. Piper, Jr. Best asymptotic bounds for truncation error in sampling expansions of bandlimited signals. IEEE Transactions Information Theory, Vol. IT-21, pp. 687–690, 1975.

[1124] H.S. Piper, Jr. Bounds for truncation error in sampling expansions of finite energy band limitedsignals. IEEE Transactions Information Theory, Vol. IT–21, pp. 482–485, 1975.

[1125] J.W. Pitton, W.L.J. Fox, L.E. Atlas, J.C. Luby, and P.J. Loughlin. Range-Doppler processingwith the cone kernel time-frequency representation communications, computers and signalprocessing, 1991., IEEE Pacific Rim Conference on Vol. 2, pp. 799–802, 1991.

[1126] J.W. Pitton and L.E. Atlas. Discrete-time implementation of the cone-kernel time-frequencyrepresentation. IEEE Transactions on Signal Processing, Vol. 43(8), pp. 1996–1998, 1995.

[1127] K. Piwerneta. A posteriori compensation for rigid body motion in holographic interferometryby means of a Moiré technique. Opt. Acta, Vol. 24, pp. 201–209, 1977.

[1128] E. Plotkin, L. Roytman, and M.N.S. Swamy. Non-uniform sampling of bandlimited modulatedsignals. Signal Processing, Vol. 4, pp. 295–303, 1982.

[1129] E. Plotkin, L. Roytman, and M.N.S. Swamy. Reconstruction of nonuniformly sampledbandlimited signals and jitter error reduction. Signal Processing, Vol. 7, pp. 151–160, 1984.

[1130] T. Pogány. On a very tight truncation error bound for stationary stochastic processes. IEEETransactions Signal Processing, Vol. 39, No. 8, pp. 1918–1919, 1991.

[1131] R.J. Polge, R.D. Hays, and L. Callas. A direct and exact method for computing the transferfunction of the optimum smoothing filter. IEEE Transactions Automatic Control, Vol. AC-18,pp. 555–556, 1973.

[1132] H.O. Pollak. Energy distribution of bandlimited functions whose samples on a half line vanish.Journal Math. Anal., Applied, Vol. 2, pp. 299–332, 1961.

[1133] Polybius of Megalopolis, World History, translated by H. J. Edwards.[1134] B. Porat. ARMA spectral estimation of time series with missing observations. IEEE

Transactions Information Theory, Vol. IT-30, No. 6, pp. 823–831, 1984.[1135] B. Porter and J.J. D’Azzo. Algorithm for closed-loop eigenstructure assignment by state

feedback in multivariable linear systems. International J. Control, Vol. 27, pp. 943–947,1978.

[1136] R.P. Porter and A.J. Devaney. Holography and the inverse source problem. Journal of theOptical Society America, Vol. 72, pp. 327–330, 1982.

[1137] M. Pourahmadi. A sampling theorem for multivariate stationary processes. JournalMultivariate Anal., Vol. 13, pp. 177–186, 1983.

[1138] F.D. Powell. Periodic sampling of broad-band sparse spectra. IEEE Transactions Acoustics,Speech, Signal Processing, Vol. ASSP-31, pp. 1317–1319, 1983.

[1139] M. Pracentini and C. Cafforio. Algorithms for image reconstruction after nonuniformsampling. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP–35, No. 8,pp. 1185–1189, 1987.

[1140] S. Prasad. Digital superresolution and the generalized sampling theorem, Journal of theOptical Society of America A – Optics, Image Science and Vision, Vol. 24(2), pp. 311–325,2007.

[1141] P.M. Prenter. Splines and Variational Methods. John Wiley, New York, 1975.[1142] R.T. Prosser. A multi-dimensional sampling theorem. Journal Math. Analysis Applied, Vol. 16,

pp. 574–584, 1966.[1143] R. Prost and R. Goutte. Deconvolution when the convolution kernel has no inverse. IEEE

Transactions Acoust., Speech, Signal Processing, pp. 542–549, 1977.


726 REFERENCES

[1144] M. Protzmann and H. Boche. Convergence proof for the algorithm by Papoulis and Gerchberg.Frequenz, Vol. 52(9–10), pp. 175–182, 1998.

[1145] E.Z. Psarakis, V.G. Mertzios, and G.P. Alexiou. Design of two-dimensional zero phase FIR fanfilters via the McClellan transform. IEEE Transactions on Circuits and Systems, Vol. 37(1),pp. 10–16, 1990.

[1146] E.Z. Psarakis and G.V. Moustakides. Design of two-dimensional zero-phase FIR filters via thegeneralized McClellan transform. IEEE Transactions on Circuits and Systems, Vol. 38(11),pp. 1355–1363, 1991.

Q[1147] S. Qazi, A. Georgakis, L.K. Stergioulas, and M. Shikh-Bahaei. Interference suppression in

the wigner distribution using fractional Fourier transformation and signal synthesis. IEEETransactions on Signal Processing, Vol. 55(6), Part 2, pp. 3150–3154, 2007.

R[1148] S.A. Rabee, B. Sharif, B.S, and S. Sali. Distributed power control algorithm in cellular radio

systems using projection onto convex sets 2001 Vehicular Technology Conference. VTC 2001Fall. IEEE VTS 54th, Vol. 2, pp. 757–761, 2001.

[1149] L.R. Rabiner and R.W. Schafer. Digital Processing of Speech Signals. Prentice-Hall,Englewood Cliffs, NJ, 1978.

[1150] D. Radbel and R.J. Marks II. An FIR estimation filter based on the sampling theorem. IEEETransactions Acoust., Speech, Signal Processing, Vol. ASSP-33, pp. 455–460, 1985.

[1151] R. Radzyner and P.T. Bason. An error bound for Lagrange interpolation of low pass functions.IEEE Transactions Information Theory, Vol. IT-18, pp. 669–671, 1972.

[1152] J.R. Ragazzini and G.F. Franklin. Sampled Data Control Systems. McGraw-Hill, New York,1958.

[1153] Y. Rahmat-Samii and R. Cheung. Nonuniform sampling techniques for antenna applications.IEEE Transactions Antennas & Propagation, Vol. AP-35, No. 3, pp. 268–279, 1987.

[1154] P.K. Rajan. A study on the properties of multidimensional Fourier transforms. IEEETransactions Circuits & Systems, Vol. CAS-31, pp. 748–750, 1984.

[1155] A. Ralston and P. Rabinowitz. A First Course in Numerical Analysis, 2nd ed. McGraw Hill,New York, 1978.

[1156] Dinakar Ramakrishnan and Robert J. Valenza. Fourier Analysison Number Fields. Springer,1998.

[1157] Jayakumar Ramanathan. Methods of Applied Fourier Analysis. Birkhäuser Boston, 1998.[1158] K.R. Rao and P. Yip. Discrete Cosine Transform: Algorithms, Advantages, Applications.

Academic Press, Boston, 1990.[1159] M.D. Rawn. Generalized sampling theorems for Bessel type transforms of bandlimited

functions and distributions. SIAM J. Applied Math., Vol. 49, No. 2, pp. 638–649, 1989.[1160] M.D. Rawn. On nonuniform sampling expansions using entire interpolating functions and

on the stability of Bessel-type sampling expansions. IEEE Transactions Information Theory,Vol. 35, No. 3, 1989.

[1161] M.D. Rawn. A stable nonuniform sampling expansion involving derivatives. IEEETransactions Information Theory, Vol. 35, No. 6, 1989.

[1162] Lord Rayleigh. On the character of the complete radiation at a given temperature. Phil. Mag.,series 5, Vol 27, 1889; reprinted in Scientific Papers, Cambridge University Press, Cambridge,England, 1902; later published by Dover Publications, New York, Vol. 3, p. 273, 1964.

[1163] M.G. Raymer. The Whittaker-Shannon sampling theorem for experimental reconstruction offree-space wave packets. Journal of Modern Optics, Vol. 44(11–12), pp. 2565–2574, 1997.

[1164] M. Reed and B. Simon. Methods and Modern Mathematical Physics. IV Analysis ofOperators. Academic Press, New York, 1978.

[1165] G.J. Ren and Y.M. Shi. Asymptotic behaviour of dynamic systems on time scales. Journal ofDifference Equations and Applications, Vol. 12(12), pp. 1289–1302, 2006.

[1166] F.M. Reza. An Introduction to Information Theory. McGraw-Hill, New York, 1961.


REFERENCES 727

[1167] A. Requicha. The zeros of entire functions: Theory and engineering applications. Proceedingsof the IEEE, Vol. 68, No. 3, pp. 308–328, 1980.

[1168] A. Restrepo, L.F. Zuluaga, and L.E. Pino. Optimal noise levels for stochastic resonance.Acoustics, Speech, and Signal Processing, 1997. ICASSP–97, 1997 IEEE InternationalConference on Vol. 3, pp. 2365–2368, 1997.

[1169] D.R. Rhodes. The optimum lines source for the best mean-square approximation to a givenradiation pattern. IEEE Transactions Antennas & Propagation, pp. 440–446, 1963.

[1170] D.R. Rhodes. A general theory of sampling synthesis. IEEE Transactions Antennas &Propagation, pp. 176–181, 1973.

[1171] W.T. Rhodes. Acousto-optical signal processing: Convolution and correlation. ProceedingsIEEE, Vol. 69, pp. 65–79, 1981.

[1172] W.T. Rhodes. Space-variant optical systems and processing. In Applications of OpticalFourier Transforms, H. Stark, editor, Academic Press, New York, 1982.

[1173] S.O. Rice Mathematical analysis of random noise. Bell System Technical J., Vol. 23,pp. 282–332, 1944.

[1174] S.O. Rice Mathematical analysis of random noise. Bell System Technical J., Vol. 24,pp. 46–156, 1945.

[1175] S. Ries and W. Splettstößer. On the approximation by truncated sampling series expansions.Signal Processing, Vol. 7, pp. 191–197, 1984.

[1176] S. Ries and R.L. Stens. A localization principle for the approximation by sampling series.In Proceedings of the International Conference on the Theory of Approximation of Functions(Kiev, USSR), Moscow; Nauka, pp. 507–509, 1983.

[1177] S. Ries and R.L. Stens.Approximation by generalized sampling series. In Constructive Theoryof Functions (Proceedings of Conference at Varna, Bulgaria, 1984), Bl. Sendov et al., editor,Sofia, Publishing House Bulgarian Acad. Sci., pp. 746–756, 1984.

[1178] A.W. Rihaczek. Signal energy distribution in time and frequency. IEEE Transactions Inform.Theory, IT–14, pp. 369–374, 1968.

[1179] C.L. Rino. Bandlimited image restoration by linear mean-square estimation. Journal of theOptical Society America, Vol. 59, pp. 547–553, 1969.

[1180] C.L. Rino. The application of prolate spheroidal wave functions to the detection and estimationof bandlimited signals. Proceedings IEEE, Vol. 58, pp. 248–249, 1970.

[1181] J. Riordan.Combinatorial Identities. Wiley & Sons, New York, 1968.[1182] O. Robaux. Application of sampling theorem for restitution of partially known objects. 2.

numerical methods. Optica Acta, Vol. 17(11), p. 811, 1970.[1183] O. Robaux. Use of Sampling theorem for reconstruction of partially known objects. 3.

decomposition of spectra. Optica Acta, Vol. 18(7), p. 523, 1971.[1184] Allan H. Robbins, Wilhelm Miller, Circuit Analysis: Theory & Practice (2nd Edition),

Delmar Thomson Learning, 1999.[1185] J.B. Roberts and D.B.S. Ajmani. Spectral analysis of randomly sampled signals using

a correlation-based slotting technique. Proceedings IEEE, Vol. 133, Pt. F, pp. 153–162,1986.

[1186] J.B. Roberts and M. Gaster. Rapid estimation of spectra from irregularly sampled records.Proceedings IEEE, Vol. 125, pp. 92–96, 1978.

[1187] J.B. Roberts and M. Gaster. On the estimation of spectra from randomly sampled signals –a method of reducing variability. Proceedings of the Royal Society London, Vol. A371,pp. 235–258, 1980.

[1188] Gregory S. Rohrer, Structure and Bonding in Crystalline Materials. Cambridge UniversityPress, 2001.

[1189] N. Rose. Mathematical Maxims and Minims, Rome Press Inc., 1988.[1190] A. Röseler. Zur Berechnung der optischen abbildung bei teilkohärenter beleuchtung mit hilfe

des sampling–theorems. Opt. Acta, Vol. 16, pp. 641–651, 1969.[1191] A. Roshan-Ghias and M.B. Shamsollahi, and M. Mobed et al., Estimation of modal parameters

using bilinear joint time-frequency distributions. Mechanical Systems and Signal Processing.Vol. 21(5), pp. 2125–2136, 2007.


728 REFERENCES

[1192] G. Ross. Iterative methods in information processing for object restoration. Opt. Acta,pp. 1523–1542, 1982.

[1193] Hugh Ross, Beyond the Cosmos: The Extra-Dimensionality of God , Navpress PublishingGroup; 2nd Expand edition 1999.

[1194] E. Roy, P.Abraham, S. Montresor, and J.L. Saumett. Comparison of time-frequency estimatorsfor peripheral embolus detection. Ultrasound in Medicine and Biology,Vol. 26(3), pp. 419–4232000.

[1195] S.H. Roy, P. Bonato, and M. Knaflitz. EMG assessment of back muscle function during cyclicallifting. Journal of Electromyography and Kinesiology. Vol 8(4), pp. 233–245, 1998.

[1196] Y.A. Rozanov. To the extrapolation of generalized random stationary processes. Theor.Probability Applied, Vol. 4, p. 426, 1959.

[1197] D.B. Rozhdestvenskii. Sampling and the discretization theorem. Automation and RemoteControl, Vol. 67(12), pp. 1991–2001, 2006.

[1198] W. Rozwoda, C.W. Therrien, and J.S. Lim. Novel method for nonuniform frequency-samplingdesign of 2-D FIR filters. In Proceedings ICASSP’88, 1988.

[1199] D.S. Ruchkin. Linear reconstruction of quantized and sampled random signals. IRETransactions Communication Systems, Vol. CS–9, 1961.

[1200] Walter Rudin. Fourier Analysis on Groups. Wiley-Interscience, 1990.[1201] A. Rundquist, A. Efimov, and D.H. Reitze. Pulse shaping with the Gerchberg-Saxton

algorithm. Journal of the Optical Society of America B – Optical Physics, Vol. 19(10),pp. 2468–2478, 2002.

[1202] C.K. Rushforth and R.L. Frost. Comparison of some algorithms for reconstructing space-limited images. Journal of the Optical Society America, Vol. 70, pp. 1539–1544, 1980.

[1203] C.K. Rushforth and R.W. Harris. Restoration, resolution, and noise. Journal of the OpticalSociety America, Vol. 58, pp. 539–545, 1968.

[1204] F.D. Russell and J.W. Goodman. Nonredundant arrays and postdetection processing foraberration compensation in incoherent imaging. Journal of the Optical Society America,Vol. 61, pp. 182–191, 1971.

S[1205] M.S. Sabri and W. Steenaart. An approach to bandlimited signal extrapolation: the

extrapolation matrix. IEEE Transactions Circuits & Systems, Vol. CAS–25, pp. 74–78, 1978.[1206] R. Sahkaya, Y. Gao, and G. Saon. Fractional Fourier transform features for speech recognition

Proceedings. (ICASSP ’04). IEEE International Conference on Acoustics, Speech, and SignalProcessing, Vol. 1, pp. I–529–32, 2004.

[1207] R.A.K. Said and D.C. Cooper. Crosspath real-time optical correlator and ambiguity functionprocessor. Proceedings Institute Elec. Engineering Vol. 120, pp. 423–428, 1973.

[1208] S.H. Saker. Oscillation of nonlinear dynamic equations on time scales. Applied Mathematicsand Computation, Vol. 148(1), pp. 81–91, 2004.

[1209] S.H. Saker. Oscillation of second-order nonlinear neutral delay dynamic equations on timescales. Journal of Computational and Applied Mathematics, Vol. 187(2), pp. 123–141, 2006.

[1210] B.E.A. Saleh. A priori information and the degrees of freedom of noisy images. Journal ofthe Optical Society America, Vol. 67, pp. 71–76, 1977.

[1211] B.E.A. Saleh and M.O. Freeman. Optical transformations. In Optical Signal Processing.J.L. Horner, editor, Academic Press, New York, 1987.

[1212] F.V. Salina, N.D.A. Mascarenhas, and P.E. Cruvinel. A comparison of POCS algorithms fortomographic reconstruction under noise and limited view. Proceedings Brazilian Symposiumon Computer Graphics and Image Processing, 2002. pp. 342–346, 2002.

[1213] F.V. Salina and N.D.A. Mascarenhas. A Hybrid Estimation Theoretic-POCS Method forTomographic Image Reconstruction. 18th Brazilian Symposium on Computer Graphics andImage Processing, 2005. SIBGRAPI 2005. pp. 220–224, 2005.

[1214] M. Salerno, G. Orlandi, G. Martinelli, and P. Burrascano. Synthesis of acoustic well-loggingwaveforms on an irregular grid. Geophysical Prospection, Vol. 34, No. 8, pp. 1145–1153,1986.


REFERENCES 729

[1215] C. Sanchez-Avila. An adaptive regularized method for deconvolution of signals with edgesby convex projections. IEEE Transactions on Signal Processing, Vol. 42(7), pp. 1849–1851,1994.

[1216] C. Sanchez-Avila and J.A. Garcia-Moreno. An adaptive LSQR algorithm for computingdiscontinuous solutions in deconvolution problems. Mathematics and Computers inSimulation, Vol. 50(1–4), pp. 323–329, 1999.

[1217] I.W. Sandberg. On the properties of some systems that distort signals – I. Bell Syst. Tech. J.,pp. 2033–2046, 1963.

[1218] J. Sanz and T. Huang. On the Gerchberg - Papoulis algorithm. IEEE Transactions on Circuitsand Systems, Vol. 30(12), pp. 907–908, 1983.

[1219] J.L.C. Sanz. On the reconstruction of bandlimited multidimensional signals from algebraicsampling contours. Proceedings IEEE, Vol. 73, pp. 1334–1336, 1985.

[1220] Vidi Saptari. Fourier Transform Spectroscopy Instrumentation Engineering. InternationalSociety for Optical Engineering (SPIE), 2003.

[1221] T.K. Sarkar, D.D. Weiner, and V.K. Jain. Some mathematical considerations in dealing withthe inverse problem. IEEE Transactions Antennas & Propagation, Vol. AP-29, pp. 373–379,1981.

[1222] K. Sasakawa. Application of Miyakawa’s Multidimensional Sampling Theorem (Japanese).Prof. Group on Inform. Theory, Institute Electron. Commun. Engineering Japan, I: no. I, 1960;II: no. 9, 1960; III: no. 2, 1961; IV: no. 6, 1961; V: no. 1, 1962.

[1223] Y. Sasaki and K. Teramoto. Improved satellite ground resolution for sea-ice observationusing an inversion method and a priori information. IEEE Journal of Oceanic Engineering.Vol. 31(1), pp. 219–229, 2006.

[1224] P. Sathyanarayana, P.S. Reddy, and M.N.S. Swamy. Interpolation of 2-D signals. IEEETransactions Circuits & Systems, Vol. 37, No. 5, pp. 623–631, 1990.

[1225] K.D. Sauer and J.P. Allebach. Iterative reconstruction of bandlimited images from non-uniformly spaced samples. IEEE Transactions Circuits & Systems, Vol. 34, pp. 1497–1505,1987.

[1226] R.W. Schafer, R.M. Mersereau, and M.A. Richards. Constrained iterative restorationalgorithms. Proceedings IEEE, pp. 432–450, 1981.

[1227] R.W. Schafer and L.R. Rabiner. A digital signal processing approach to interpolation.Proceedings IEEE, Vol. 61, pp. 692–702, 1973.

[1228] S.A. Schelkunoff. Theory of antennas of arbitrary size and shape. Proceedings IRE,pp. 493–521, 1941.

[1229] W. Schempp. Radar ambiguity functions, the Heisenberg group, and holomorphic theta series.Proceedings America Math. Society Vol. 92, pp. 103–110, 1984.

[1230] W. Schempp. Gruppentheoretische aspekte der signal übertragung und der kardinaleninterpolations splines I. Math. Meth. Applied Sci., Vol. 5, pp. 195–215, 1983.

[1231] J.L. Schiff and W.J. Walker. A sampling theorem for analytic functions. Proceedings of theAmerican Mathematical Society, Vol. 99(4), pp. 737–740, 1987.

[1232] J.L. Schiff and W.J. Walker. A sampling theorem and wintner results on Fourier coefficients.Journal of Mathematical Analysis and Applications, Vol. 133(2), pp. 466–471, 1988.

[1233] J.L. Schiff and W.J. Walker. A sampling theorem for a class of pseudoanalytic functions.Proceedings of the American Mathematical Society, Vol. 111(3), pp. 695–699, 1991.

[1234] R.J. Schlesinger and V.B. Ballew. An application of the sampling theorem to data collectionin a computer integrated manufacturing environment. International Journal of ComputerIntegrated Manufacturing, Vol. 2(1), pp. 15–22, 1989.

[1235] Dietrich Schlichthärle. Digital Filters: Basics and Design. Springer, 2000.[1236] I.J. Schoenberg. Contributions to the problem of approximation of equidistant data by analytic

functions. Part a: On the problem of smoothing or graduation. A first class of analyticapproximation formulae. Quart. Applied Math., Vol. 4, pp. 45–99, 1946.

[1237] I.J. Schoenberg. Cardinal interpolation and spline functions. Journal Approx. Theory 2,pp. 167–206, 1969.

[1238] A. Schönhage. Approximationstheorie. de Gruyter, Berlin – New York, 1971.


730 REFERENCES

[1239] Hartmut Schroder and Holger Blume. One- and Multidimensional Signal Processing:Algorithms and Applications in Image Processing. John Wiley & Sons, 2001.

[1240] L.L. Schumaker. Spline Functions: Basic Theory. Wiley, New York, 1981.[1241] G. Schwierz, W. Härer, and K. Wiesent. Sampling and discretization problems in X-ray CT.

In Mathematical Aspects of Computerized Tomography, Springer-Verlag, Berlin,1981.

[1242] H.J. Scudder. Introduction to computer aided tomography. Proceedings IEEE, Vol. 66,pp. 628–637, 1978.

[1243] M. Sedletskii. Fourier Transforms and Approximations. CRC, 2000.[1244] Robert T. Seeley. An Introduction to Fourier Series and Integrals. Dover Publications

2006.[1245] J. Segethova. Numerical construction of the Hill function. SIAM J. Numer. Anal. Vol. 9,

pp. 199–204, 1972.[1246] K. Seip. An irregular sampling theorem for functions bandlimited in a generalized sense.

SIAM J. Applied Math., Vol. 47, pp. 1112–1116, 1987.[1247] K. Seip. A note on sampling bandlimited stochastic processes. IEEE Transactions Information

Theory, Vol. 36, No. 5, p. 1186, 1990.[1248] A. Sekey. A computer simulation study of real-zero interpolation. IEEE Transactions Audio

Electroacoustics, Vol. 18, p. 43, 1970.[1249] I.W. Selesnick. Interpolating multiwavelet bases and the sampling theorem. IEEETransactions

on Signal Processing, Vol. 47(6), pp. 1615–1621, 1999.[1250] M. De La Sen. Nonperiodic sampling and model matching. Electron. Letters, Vol. 18,

pp. 311–313, 1982.[1251] M. De La Sen and S. Dormido. Nonperiodic sampling and identifiability. Electron. Letters,

Vol. 17, pp. 922–925, 1981.[1252] M. De La Sen and M.B. Pay. On the use of adaptive sampling in hybrid adaptive error models.

Proceedings IEEE, Vol. 72, pp. 986–989, 1984.[1253] M.I. Sezan and H. Stark. Image restoration by method of convex set projections: Part II –

Applications and Numerical Results. IEEE Transactions Med. Imaging, Vol MI-1, pp. 95–101,1982.

[1254] M. Ibrahim Sezan, Henry Stark and Shu-Jen Yeh. Projection method formulations of Hopfield-type associative memory neural networks. Applied Optics, Vol. 29, No. 17, pp. 2616–2622,1990.

[1255] M. Ibrahim Sezan and Henry Stark. Tomographic image reconstruction from incomplete viewdata by convex projections and direct Fourier inversion. IEEE Transactions Medical Imaging,Vol. MI–3, No. 2, pp. 91–98, 1984.

[1256] C.E. Shannon.Amathematical theory of communication. Bell Systems Tech. J.,Vol. 27, pp. 379and 623, 1948.

[1257] C.E. Shannon. Communications in the presence of noise. Proceedings IRE, Vol. 37, pp. 10–21,1949.

[1258] C.E. Shannon and W. Weaver. The Mathematical Theory of Communication. Universityof Illinois Press, Urbana, IL, 1949.

[1259] H.S. Shapiro. Smoothing and Approximation of Functions. Van Nostrand Reinhold,New York, 1969.

[1260] H.S. Shapiro. Topics in Approximation Theory. Lecture Notes in Mathematics, Vol. 187,Springer-Verlag, Berlin - Heidelberg – New York, 1971.

[1261] H.S. Shapiro and R.A. Silverman. Alias free sampling of random noise. Journal SIAM, Vol. 8,pp. 225–236, 1960.

[1262] K.K. Sharma and S.D. Joshi. Signal reconstruction from the undersampled signal samplesOptics Communications, Vol. 268(2), pp. 245–252, 2006.

[1263] L. Shaw. Spectral estimates from nonuniform samples. IEEE Transactions AudioElectroacoustics, Vol. AU–19, 1970.

[1264] R.G. Shenoy and T.W. Parks. An optimal recovery approach to interpolation. IEEETransactions Signal Processing, Vol. 40, No. 6, pp. 1987–1988, 1992.


REFERENCES 731

[1265] C.E. Shin, S.Y. Chung, and D. Kim. General sampling theorem using contour integral. Journalof Mathematical Analysis and Application, Vol. 291(1), pp. 50–65, 2004.

[1266] J.H. Shin, J.H. Jung, and J.R. Paik. Spatial interpolation of image sequences usingtruncated projections onto convex sets. IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences, Vol. E82A(6), pp. 887–892, 1999.

[1267] Eric Stade. Fourier Analysis. Wiley-Interscience, 2005.[1268] Elias M. Stein and Rami Shakarchi. Fourier Analysis: An Introduction. (Princeton Lectures

in Analysis. Volume 1). Princeton University Press, 2003.[1269] Elias M. Stein and Guido Weiss. Introduction to Fourier Analysis on Euclidean Spaces.

Princeton University Press, 1971.[1270] A. Stern and B. Javidi. Improved-resolution digital holography using the generalized sampling

theorem for locally band-limited fields. Journal of the Optical Society of America A – Optics,Image Science and Vision, Vol. 23(5), pp. 1227–1235, 2006.

[1271] A. Stern. Sampling of linear canonical transformed signals. Signal Processing, Vol. 86(7),pp. 1421–1425, 2006.

[1272] A. Sherstinsky and C.G. Sodini. A programmable demodulator for oversampled analog-to-digital modulators. IEEE Transactions Circuits & Systems,Vol. CAS-37, No. 9, pp. 1092–1103,1990.

[1273] S. Shirani, F. Kossentini, and R. Ward. Reconstruction of baseline JPEG coded images in errorprone environments. IEEE Transactions Image Processing, Vol. 9, No.7, pp. 1292–1299, 2000.

[1274] F. S. Shoucair. Joseph Fourier’s analytical theory of heat: a legacy to science and engineering.IEEE Transactions on Education, Vol. 32, pp. 359–366, 1989.

[1275] Emil Y. Sidky, Chien-Min Kao, and Xiaochuan Pan. Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT. Journal of X-Ray Science and Technology,Vol. 14(2), pp. 119–139, 2006.

[1276] G. Simmons, Calculus Gems, New York: Mcgraw Hill, Inc., 1992.[1277] R. Simon. Krishnan and the sampling theorem. Current Science, Vol. 75(11), pp. 1239–1245,

1998.[1278] G. Sinclair, J. Leach, P. Jordan, et al. Interactive application in holographic optical tweezers of a

multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping. Optics Express,Vol. 12(8), pp. 1665–1670, 2004.

[1279] N.K. Sinha and G.J. Lastman. Identification of continuous-time multivariable systems fromsampled data. International J. Control, Vol. 35, pp. 117–126, 1982.

[1280] D. Slepian. Prolate spheroidal wave functions Fourier analysis and uncertainty IV: Extensionsto many dimensions; generalized prolate spheroidal wave functions. Bell Systems Tech. J.,Vol. 43, pp. 3009–3057, 1964.

[1281] D. Slepian. Analytic solution of two apodization problems. Journal of the Optical SocietyAmerica, Vol. 55, pp. 1110–1115, 1965.

[1282] D. Slepian. Some asymptotic expansions for prolate spheroidal wave functions. Journal Math.,Phys. Vol. 44, No. 2, pp. 99–140, 1965.

[1283] D. Slepian. On bandwidth. Proceedings IEEE, Vol. 64, pp. 292–300, 1976.[1284] D. Slepian. Prolate spheroidal wave functions, Fourier analysis and uncertainty – V: The

discrete case. Bell Systems Tech. J., Vol. 57, pp. 1371–1430, 1978.[1285] D. Slepian and H.O. Pollak. Prolate spheroidal wave functions Fourier analysis and uncertainty

I. Bell Systems Tech. J., Vol. 40, pp. 43–63, 1961.[1286] D. Slepian and E. Sonnenblick. Eigenvalues associated with prolate spheroidal wave functions

of zero order. Bell Systems Tech. J., Vol. 44, pp. 1745–1758, 1965.[1287] Robert Smedley and Garry Wiseman. Introducing Pure Mathematics. Oxford University

Press, 2001.[1288] Alexandre Smirnov. Processing of Multidimensional Signals. Springer, 1999.[1289] D.K. Smith and R.J. Marks II. Closed form bandlimited image extrapolation. Applied Optics,

Vol. 20, pp. 2476–2483, 1981.[1290] Julius O. Smith III. Mathematics of the Discrete Fourier Transform (DFT): with Audio

Applications. Second Edition. BookSurge Publishing, 2007.


732 REFERENCES

[1291] M.J. Smith, Jr. An evaluation of adaptive sampling. IEEE Transactions Automatic Control,Vol. AC–16, pp. 282–284, 1971.

[1292] T. Smith, M.R. Smith, and S.T. Nichols. Efficient sinc function interpolation technique forcenter padded data. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-38,No. 9, pp. 1512–1517, 1990.

[1293] Brian C. Smith. Fundamentals of Fourier Transform Infrared Spectroscopy. CRC Press,1995.

[1294] Ian N. Sneddon. The Use of Integral Transforms. McGraw-Hill, New York, 1972.[1295] Ian N. Sneddon. Fourier Transforms. Dover Publications, 1995.[1296] M.A. Soderstrand. Residue Number System Arithmetic: Modern Applications in Digital

Signal Processing. IEEE Press, 1986.[1297] Guy R. Sohie and George N. Maracas. Orthogonality of exponential transients. Proceedings

IEEE, Vol. 76, No. 12, pp. 1616–1618, 1988.[1298] E.A. Soldatov and E.V. Chuprunov. The Kotelnikov-Shannon sampling theorem in the

structure analysis. Crystallography Reports, Vol. 44(5), pp. 732–733, 1999.[1299] S.C. Som. Simultaneous multiple reproduction of space-limited functions by sampling of

spatial frequencies. Journal of the Optical Society America, Vol. 60, pp. 1628–1634, 1970.[1300] I. Someya. Waveform Transmission. Shukyo, Ltd., Tokyo, 1949.[1301] Young-Seog Song and Yong Hoon Lee. Formulas for McClellan transform parameters in

designing 2-D zero-phase FIR fan filters. IEEE Signal Processing Letters, Vol. 3(11), pp. 291–293, 1996.

[1302] M. Soumekh. Bandlimited interpolation from unevenly spaced sampled data. IEEETransactions Acoust., Speech, Signal Processing, Vol. ASSP-36, No. 1, pp. 110–122, 1988.

[1303] M. Soumekh. Reconstruction and sampling constraints for spiral data. IEEE TransactionsAcoust., Speech, Signal Processing, Vol. ASSP-37, pp. 882–891, 1989.

[1304] Mehrdad Soumekh. FourierArray Imaging. Prentice Hall Professional Technical Reference,1993.

[1305] J.J. Spilker. Theoretical bounds on the performances of sampled data communications systems.IRE Transactions Circuit Theory, Vol. CT-7, pp. 335–341, 1960.

[1306] W. Splettstößer. Über die Approximation stetiger Funktionen durch die klassischen und durchneueAbtastsummen mit Fehlerabschätzungen. Doctoral dissertation, RWTHAachen,Aachen,Germany, 1977.

[1307] W. Splettstößer. On generalized sampling sums based on convolution integrals. AEU, Vol. 32,No. 7, pp. 267–275, 1978.

[1308] W. Splettstößer. Error estimates for sampling approximation of non-bandlimited functions.Math. Meth. Applied Sci., Vol. 1, pp. 127–137, 1979.

[1309] W. Splettstößer. Error analysis in the Walsh sampling theorem. In 1980 IEEE InternationalSymposium on Electromagnetic Compatibility, Baltimore, Vol. 409, pp. 366–370, 1980.

[1310] W. Splettstößer. Bandbegrenzte und effektiv bandbegrenzte funktionen und ihre praediktionaus abtastwerten. Habilitationsschrift, RWTH Aachen, 1981.

[1311] W. Splettstößer. On the approximation of random processes by convolution processes.Z. Angew. Math. Mech., Vol. 61, pp. 235–241, 1981.

[1312] W. Splettstößer. Sampling series approximation of continuous weak sense stationaryprocesses. Information & Control, Vol. 50, pp. 228–241, 1981.

[1313] W. Splettstößer. On the prediction of bandlimited processes from past samples. Inform. Sci.,Vol. 28, pp. 115–130, 1982.

[1314] W. Splettstößer. Sampling approximation of continuous functions with multi-dimensionaldomain. IEEE Transactions Information Theory, Vol. IT-28, pp. 809–814, 1982.

[1315] W. Splettstößer. 75 years aliasing error in the sampling theorem. In EUSIPCOM – 83,Signal Processing: Theories and Applications (2. European Signal Processing Conference,Erlangen), H.W. Schüssler, editor. North-Holland Publishing Company, Amsterdam -New York - Oxford, 1983, pp. 1–4.

[1316] W. Splettstößer. Lineare praediktion von nicht bandbegrenzten funktionen. Z. Angew. Math.Mech. Vol. 64, pp. T393–T395, 1984.


REFERENCES 733

[1317] W. Splettstößer, R.L. Stens, and G. Wilmes. On approximation by the interpolating series ofG. Valiron. Funct. Approx. Comment. Math., Vol. 11, pp. 39–56, 1981.

[1318] W. Splettstößer and W. Ziegler. The generalized Haar functions, the Haar transform on r+,and the Haar sampling theorem. In Proceedings of the “Alfred Haar Memorial Conference,”Budapest, pp. 873–896, 1985.

[1319] T. Springer. Sliding FFT computes frequency spectra in real time. EDN Magazine,September 29, 1988, pp. 161–170.

[1320] Julien Clinton Sprott. Chaos and Time-Series Analysis. Oxford University Press, 2003.[1321] C.J. Standish. Two remarks on the reconstruction of sampled non-bandlimited functions. IBM

J. Res. Develop. Vol. 11, pp. 648–649, 1967.[1322] H. Stark. Sampling theorems in polar coordinates. Journal of the Optical Society America,

Vol. 69, pp. 1519–1525, 1979.[1323] H. Stark. Polar sampling theorems of use in optics. Proceedings SPIE, International Society

Optical Engineering, Vol. 358, pp. 24–30, 1982.[1324] H. Stark, editor. Image Recovery: Theory and Application. Academic Press, Orlando, FL,

1987.[1325] H. Stark, D. Cahana, and H. Webb. Restoration of arbitrary finite-energy optical objects from

limited spatial and spectral information. Journal of the Optical Society America, Vol. 71,pp. 635–642, 1981.

[1326] H. Stark and C.S. Sarna. Bounds on errors in reconstructing from undersampled images.Journal of the Optical Society America, Vol. 69, pp. 1042–1043, 1979.

[1327] H. Stark and C.S. Sarna. Image reconstruction using polar sampling theorems of use inreconstructing images from their samples and in computer aided tomography. Applied Optics,Vol. 18, pp. 2086–2088, 1979.

[1328] H. Stark and M. Wengrovitz. Comments and corrections on the use of polar sampling theoremsin CT. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-31, pp. 1329–1331,1983.

[1329] H. Stark and John W. Woods. Probability, Random Processes, and Estimation Theory forEngineers. Prentice-Hall, Englewood Cliffs, NJ, 1986.

[1330] H. Stark, J.W. Woods, I. Paul, and R. Hingorani. Direct Fourier reconstruction incomputer tomography. IEEE Transactions Acoust., Speech, Signal Processing, Vol. ASSP-29,pp. 237–245, 1981.

[1331] H. Stark, J.W. Woods, I. Paul, and R. Hingorani.An investigation of computerized tomographyby direct Fourier inversion and optimum interpolation. IEEE Transactions BiomedicalEngineering, Vol. BME-28, pp. 496–505, 1981.

[1332] H. Stark. Sampling theorems in polar coordinates. Journal of the Optical Society America,Vol. 69, No. 11, pp. 1519–1525, 1979.

[1333] H. Stark and Y. Yang, Vector Space Projections: A Numerical Approach to Signal andImage Processing, Neural Nets, and Optics Wiley-Interscience, New York, 1998.

[1334] R. Stasinski and J. Konrad. Linear shift-variant filtering for POCS of reconstruction irregularlysampled images. Proceedings of the 2003 International Conference on Image Processing,2003. ICIP 2003. Vol. 3, pp. III - 689–692, 2003.

[1335] O.N. Stavroudis.The Optics of Rays,Wavefronts, and Caustics.Academic Press, NewYork,1972.

[1336] R. Steele and F. Benjamin. Sample reduction and subsequent adaptive interpolation of speechsignals. Bell Systems Tech. J., Vol. 62, pp. 1365–1398, 1983.

[1337] P. Stelldinger and U. Kothe. Towards a general sampling theory for shape preservation. Imageand Vision Computing, Vol. 23(2), pp. 237–248, 1 2005.

[1338] F. Stenger.Approximations via Whittaker’s cardinal function. Journal Approx. Theory, Vol. 17,pp. 222–240, 1976.

[1339] F. Stenger. Numerical methods based on Whittaker cardinal, or sinc functions. SIAM Rev.,Vol. 23, pp. 165–224, 1981.

[1340] R.L. Stens.Approximation of duration-limited functions by sampling sums. Signal Processing,Vol. 2, pp. 173–176, 1980.


734 REFERENCES

[1341] R.L. Stens. A unified approach to sampling theorems for derivatives and Hilbert transforms.Signal Processing, Vol. 5, pp. 139–151, 1983.

[1342] R.L. Stens. Error estimates for sampling sums based on convolution integrals. Information &Control, Vol. 45, pp. 37–47, 1980.

[1343] R.L. Stens. Approximation of functions by Whittaker’s cardinal series. in GeneralInequalities 4 (Proceedings Conf. Math. Res. Institute Oberwolfach, W. Walter, ed.) BirkhäuserVerlag, Basel, pp. 137–149, 1984.

[1344] E.G. Steward. Fourier Optics: An Introduction. Dover Publications, 2004.[1345] R.M. Stewart. Statistical design and evaluation of filters for the restoration of sampled data.

Proceedings IRE, Vol. 44, pp. 253–257, 1956.[1346] D.C. Stickler. An upper bound on aliasing error. Proceedings IEEE, Vol. 55, pp. 418–419,

1967.[1347] G. Strang. Linear Algebra and Its Applications. Academic Press, New York, 1980.[1348] Gilbert Strang and Truong Nguyen. Wavelets and Filter Banks. Second Edition. Wellesley

College, 1996.[1349] R.N. Strickland, A.P. Anderson, and J.C. Bennett. Resolution of subwavelength-spaced

scatterers by superdirective data processing simulating evanescent wave illumination.Microwaves, Opt. & Acoust., Vol. 3, pp. 37–42, 1979.

[1350] G. Stigwall and S. Galt. Non-linear signal retrieval in wide-band photonic time-stretchsystems using the gerchberg-Saxton algorithm. International Topical Meeting on MicrowavePhotonics, 2006. MWP ’06. pp. 1–4, 2006

[1351] T. Strohmer and J. Tanner. Fast reconstruction methods for bandlimited functions from periodicnonuniform sampling. SIAM Journal on Numerical Analysis, Vol. 44(3), pp. 1073–1094, 2006.

[1352] J.A. Stuller. Reconstruction of finite duration signals. IEEE Transactions Information Theory,Vol. IT-18, pp. 667–669, 1972.

[1353] K.L. Su. Analog Filters, Second Edition. Springer, 2002.[1354] R. Sudhakar, R.C. Agarwal, and S.C. Dutta Roy. Fast computation of Fourier transform at

arbitrary frequencies. IEEE Transactions Circuits & Systems, Vol. CAS-28, pp. 972–980, 1982.[1355] R. Sudol and B.J. Thompson. An explanation of the Lau effect based on coherence theory.

Optical Communication, pp. 105–110, 1979.[1356] R. Sudol and B.J. Thompson. Lau effect: theory and experiment. Applied Optics,

pp. 1107–1116, 1981.[1357] H. Sugiyama. A sampling theorem with equally spaced sampling points of the negative time

axis. Mathematics of Control Signals and Systems, Vol 6(2), pp. 125–134, 1993.[1358] B. Summers, G.D. Cain. An extension to the sampling theorem for lowpass bandlimited

periodic time functions using nth order sampling schemes. IEEE Transactions onInstrumentation and Measurement, Vol. 40(6), pp. 990–993, 1991.

[1359] Hong-Bo Sun, Guo-Sui Liu, Hong Gu, and Wei-Min Su. Application of the fractional Fouriertransform to moving target detection in airborne SAR. IEEE Transactions on Aerospace andElectronic Systems, Vol. 38(4), pp. 1416–1424, 2002.

[1360] H.R. Sun and W.T. Li. Positive solutions of second-order half-linear dynamic equations ontime scales. Applied Mathematics and Computation, Vol. 158(2), pp. 331–344, 2004.

[1361] H. Sun and W. Kwok. Concealment of damaged blocks transform coded images usingprojections onto convex sets. IEEE Transactions Image Processing, Vol. 4, pp. 470–477,1995.

[1362] W.C. Sun and X.W. Zhou. Sampling theorem for wavelet subspaces: Error estimate andirregular sampling. IEEE Transactions on Signal Processing, Vol. 48(1), pp. 223–226, 2000.

[1363] W.C. Sun and Z.W. Zhou. The aliasing error in recovery of nonbandlimited signals byprefiltering and sampling. Applied Mathematics Letters, Vol. 16(6), pp. 949–954, 2003.

[1364] Y.R. Sun and S. Signell. Effects of noise and jitter in bandpass sampling. Analog IntegratedCircuits and Signal Processing, Vol. 42(1), pp. 85–97, 2005.

[1365] Zhaohui Sun, et al. Interactive optimization of 3D shape and 2D correspondence usingmultiple geometric constraints via POCS. IEEE Transactions on Pattern Analysis and MachineIntelligence, Vol. 24(4), pp. 562–569, 2002.


REFERENCES 735

[1366] H. Sundaram, S.D. Joshi, and R.K.P. Bhatt. Scale periodicity and its sampling theorem. IEEETransactions on Signal Processing, Vol. 45(7), pp. 1862–1865, 1997.

[1367] D. Sundararajan. The Discrete Fourier Transform: Theory, Algorithms and Applications.World Scientific Publishing Company, 2001.

[1368] S.K. Suslov. An Introduction to Basic Fourier Series. Springer, 2003.[1369] K. Swaminathan. Signal restoration from data aliased in time. IEEE Transactions Acoust.,

Speech, Signal Processing, Vol. ASSP-33, pp. 151–159, 1985.[1370] G.J. Swanson and E.N. Leith. Lau effect and grating imaging. Journal of the Optical Society

America, Vol. 72, pp. 552–555, 1982.[1371] S. Szapiel. Sampling theorem for rotationally symmetric systems based on dini expansion.

Opt. Letters, Vol. 6, pp. 7–9, 1981.[1372] H.H. Szu and J.A. Blodgett. Wigner distribution and ambiguity function. Optics in Four

Dimensions–1980, AIP Conf. Proceedings 65, M.A. Machado and L.M. Narducci, eds.American Institute of Physics, New York, pp. 355–381, 1980.

T[1373] P.D. Tafti, S. Shirani, and X.L. Wu. On interpolation and resampling of discrete data. IEEE

Signal Processing Letters, Vol. 13(12), pp. 733–736, 2006.[1374] S. Takata. J B Fourier in the history of thermal radiation research. Historia Sci., (2) 2 (3),

pp. 203–221, 1993.[1375] M. Takagi and E. Shinbori. High quality image magnification applying the Gerchberg-Papoulis

iterative algorithm with DCT. Systems and Computers in Japan, Vol. 25(6), pp. 80–90 1994.[1376] Y. Tanaka, T. Fujiwara, and H. Koshimizu, et al. OK-Quantization Theory and its relationship

to sampling theorem. Lecture Notes in Computer Science, Vol. 3852, pp. 479–488 2006.[1377] B. Tatian. Asymptotic expansions for correcting truncation error in transfer function

calculations. Journal of the Optical Society America, Vol. 61, pp. 1214–1224, 1971.[1378] H. Taylor and C.A. Lipson. Fourier Transforms and X-Ray Diffraction. G. Bell & Sons

Ltd., 1958.[1379] C. Tellambura. Computing the outage probability in mobile radio networks using the sampling

theorem. IEEE Transactions on Communications, Vol. 47(8), pp. 1125–1128, 1999.[1380] G.C. Temes, V. Barcilon, and F.C. Marshall III. The optimization of bandlimited systems.

Proceedings IEEE, Vol. 61, pp. 196–234, 1973.[1381] K. Teramoto. Conjugate gradient projection onto convex sets for sparse array acoustic

holography. IEICE Transactions on Fundamentals of Electronics Communications andComputer Sciences, Vol E80A(5), pp. 833–839, 1997.

[1382] Audrey Terras. Fourier Analysis on Finite Groups and Applications. Cambridge UniversityPress, 1999.

[1383] Les Thede. Practical Analog And Digital Filter Design. Artech House Publishers, 2004.[1384] M. Theis. Über eine Interpolationsformel von de la Vallée-Poussin. Math. Z., Vol. 3,

pp. 93–113, 1919.[1385] C. Thieke, T. Bortfeld,A. Niemierko, and S. Nill. From physical dose constraints to equivalent

uniform dose constraints in inverse radiotherapy planning Medical Physics. Vol. 30(9),pp. 2332–2339, 2003.

[1386] G. Thomas. A modified version of Van Cittert’s iterative deconvolution procedure. IEEETransactions Acoust., Speech, Signal Processing, Vol. ASSP-29, pp. 938–939, 1981.

[1387] J.B. Thomas. An Introduction to Statistical Communication Theory. John Wiley & Sons,Inc., New York, 1969.

[1388] J.B. Thomas and B. Liu. Error problems in sampling representations, Part 5. IEEEInternational Conv. Rec., Vol. 12, pp. 269–277, 1964.

[1389] B.J. Thompson. Image formation with partially coherent light. In Progress in Optics, E. Wolf,editor, North Holland, Amsterdam, pp. 169–230, 1969.

[1390] B.J. Thompson. Multiple imaging by diffraction techniques. Applied Optics, p. 312, 1976.[1391] J.E. Thompson and L.H. Luessen, editors. Fast Electrical and Optical Measurements,Vol. 1.

Martinus Nijhoff Publishers, 1986.


736 REFERENCES

[1392] Sir William Thomson (Lord Kelvin) and Peter Guthrie Tait. Treatise On Natural Philosophy,By Sir William Thomson And Peter Guthrie Tait, University of Michigan Library, 2001.

[1393] B. Tian et al. POCS supperresolution image reconstruction using wavelet transformProceedings of International Symposium on 2004 Intelligent Signal Processing andCommunication Systems, ISPACS 2004. pp. 67–70, 2004.

[1394] A.N. Tikhonov and V.Y. Arsenine. Solutions of Ill-Posed Problems. Wiston/Wiley,Washington, DC, 1977.

[1395] A.F. Timan. Theory of Approximation of Functions of a Real Variable. Pergamon Press,Oxford, 1963.

[1396] E.C. Titchmarsh. The zeros of certain integral functions. Proceedings London Math. Society,Vol. 25, pp. 283–302, 1926.

[1397] E.C. Titchmarsh. Introduction to the Fourier Integral. Oxford University Press, Oxford,1937.

[1398] E.C. Titchmarsh. The Theory of Functions, 2nd ed. University Press, London, 1939.[1399] E.C. Titchmarsh. Introduction to the Theory of Fourier Integrals (2nd Edition). Clarendon

Press, Oxford, 1948.[1400] D.E. Todd. Sampled data reconstruction of deterministic bandlimited signals. IEEE

Transactions Information Theory, Vol. IT-19, pp. 809–811, 1973.[1401] Georgi P. Tolstov. Fourier Series. Dover Publications, 1976.[1402] Lex Tokyo, Yo Sakakibara, Alan Gleason. Who Is Fourier?: A Mathematical Adventure,

Language Research Foundation, 1995.[1403] G. Toraldo diFrancia. Super-gain antennas and optical resolving power. Suppl. Nuovo Cimento,

pp. 426–438, 1952.[1404] G. Toraldo diFrancia. Resolving power and information. Journal of the Optical Society

America, Vol 45, pp. 497–501, 1955.[1405] G. Toraldo diFrancia. Directivity, super-gain and information. IRE Transactions Antennas &

Propagation, Vol. AP-4, pp. 473–478, 1956.[1406] G.Toraldo diFrancia. La diffrazione della luce. Einaudi Bornghieri, Torino, 1958.[1407] G. Toraldo diFrancia. Degrees of freedom of an image. Journal of the Optical Society America,

Vol. 59, pp. 799–804, 1969.[1408] R.H. Torres. Spaces of Sequences, Sampling Theorem, and Functions of Exponential Type.

Studia Mathematica, Vol. 100(1), pp. 51–74, 1991.[1409] R.T. Torres, P. Pellat-Finet, andY. Torres. Sampling theorem for fractional bandlimited signals:

A self-contained proof. Application to digital holography. IEEE Signal Processing Letters,Vol. 13(11), pp. 676–679, 2006.

[1410] Hans Triebel. Fractals and Spectra: Related to Fourier Analysis and Function Spaces.Birkhäuser Basel, 1997.

[1411] Roald M. Trigub and Eduard S. Belinsky. Fourier Analysis and Approximation ofFunctions. Springer, 2004.

[1412] H.J. Trussel, L.L. Arnder, P.R. Morand, and R.C. Williams. Corrections for nonuniformsampling distortions in magnetic resonance imagery. IEEE Transactions Medical Imaging,Vol. MI-7, No. 1, pp. 32–44, 1988.

[1413] C.C. Tseng. Design of two-dimensional FIR digital filters by McClellan transform andquadratic programming. IEE Proceedings onVision, Image and Signal Processing,Vol. 148(5),pp. 325–331, 2001.

[1414] Shiao-Min Tseng. Noise LevelAnalysis of Linear RestorationAlgorithms for BandlimitedSignals. Ph.D. thesis, University of Washington, 1984.

[1415] John Hudsion Tiner. Louis Pasteur – Founder of Modern Medicine. Milford, MI: MottMedia, Inc., p. 75, 1990.

[1416] S. Tsekeridou and I. Pitas. MPEG-2 error concealment based on block-matching principles.IEEE Transactions Circuits Syst. Video Technol., Vol. 10, pp. 646–658, 2000.

[1417] J. Tsujiuchi. Correction of optical images by compensation of aberrations and by spatialfrequency filtering. In Progress in Optics, E. Wolf, editor. North-Holland, Amsterdam,pp. 131–180, 1963.


REFERENCES 737

[1418] Y. Tsunoda and Y. Takeda. High density image-storage holograms by a random phase samplingmethod. Applied Optics, Vol. 13, pp. 2046–2051, 1974.

[1419] P. Turán. The Work of Alfréd Rényi. Matematikai Lapok 21, pp. 199–210, 1970.[1420] B. Turner. Fourier’s seventeen lines problem. Math. Mag., Vol. 53(4), pp. 217–219, 1980.[1421] J. Turunen, A. Vasara, and A.T. Friberg. Propagation invariance and self-imaging in variable

coherence optics. Journal of the Optical Society America A, Vol. 8, pp. 282–289, 1991.[1422] J. Turunen,A. Vasara, J. Werterholm, andA. Salin. Strip-geometry two-dimensional Dammann

gratings. Optical Communication, Vol. 74, pp. 245–252, 1989.[1423] Tzafestas Multidimensional Systems. CRC, 1986.

U[1424] Kazunori Uchida. Spectral domain method and generalized sampling theorems. Transactions

of IEICE, Vol. E73, No. 3, pp. 357–359, 1990.[1425] T. Umemoto, S. Fujisawa, and T. Yoshida. Constant Q-value filter banks with spectral

analysis using LMS algorithm. Proceedings of the 37th SICE Annual Conference. (ISICE ’98).pp. 1019–1024, 1998.

[1426] M. Unser, A. Aldroubi, and M. Eden Polynomial spline signal approximations: Filterdesign and asymptotic equivalence with Shannon’s sampling theorem. IEEE TransactionsInformation Theory, Vol. IT-38, No. 1, 1992.

[1427] H.P. Urbach. Generalised sampling theorem for band-limited functions. Mathematical andComputer Modelling, Vol. 38(1–2), pp. 133–140, 2003.

[1428] S. Urieli et al. Optimal reconstruction of images from localized phase. IEEE Transactions onImage Processing, Vol. 7(6), pp. 838–853, 1998.

V[1429] P.P. Vaidyanathan and Vincent C. Liu. Classical sampling theorems in the context of multirate

and polyphase digital filter bank structures. IEEE Transactions Acoust., Speech, SignalProcessing, Vol. ASSP-36, No. 9, pp. 1480–1495, 1988.

[1430] P.P. Vaidyanathan. Multirate Systems And Filter Banks. Prentice Hall, 1992.[1431] C. Vaidyanathan and K.M. Buckley. A sampling theorem for EEG electrode configuration.

IEEE Transactions on Biomedical Engineering, Vol. 44(1), pp. 94–97, 1997.[1432] P.P. Vaidyanathan. Generalizations of the sampling theorem: seven decades after Nyquist.

IEEE Transactions on Circuits and Systems I – Fundamental Theory and Applications,Vol. 48(9), pp. 1094–1109, 2001.

[1433] Lucia Valbonesi and Ansari, Frame-based approach for peak-to-average power ratio reductionin OFDM, IEEE Transactions on Communications. Vol. 54(9), pp. 1604–1613, 2006.

[1434] P.H. Van Cittert. Zum einfluss der splatbreite auf die intensitat-swerteilung in spektrallinienII. Z. Phys., Vol. 69, pp. 298–308, 1931.

[1435] L. Valbonesi and R. Ansari. POCS-based frame-theoretic approach for peak-to-average powerratio reduction in OFDM. IEEE 60th Vehicular Technology Conference, 2004. Vol. 1, pp. 631–634, 2004.

[1436] E. Van der Ouderaa and J. Renneboog. Some formulas and application of nonuniform samplingof bandwidth limited signal. IEEE Transactions Instrumentation & Measurement, Vol.IM–37,No. 3, pp. 353–357, 1988.

[1437] P.J. Van Otterloo and J.J. Gerbrands. A note on sampling theorem for simply connected closedcontours. Information & Control, Vol. 39, pp. 87–91, 1978.

[1438] G.A. Vanasse and H. Sakai. Fourier spectroscopy. In Progress in Optics, E. Wolf, editor.North-Holland, Amsterdam, 1967.

[1439] A. VanderLugt. Optimum sampling of Fresnel transforms. Applied Optics, Vol. 29, No. 23,pp. 3352–3361, 1990.

[1440] A.B. VanderLugt. Signal detection by complex spatial filtering. IEEE TransactionsInformation Theory, Vol. IT-10, pp. 2–8, 1964.

[1441] P.J. Vanotterloo and J.J. Gerbrands. Note on a Sampling Theorem for Simply ConnectedClosed Contours. Information and Control, Vol. 39(1), pp. 87–91, 1978.


738 REFERENCES

[1442] Harry L. Van Trees. Detection, Estimation, and Modulation Theory, Part I. Wiley-Interscience; Reprint edition, 2001.

[1443] M.E. Van Valkenburg, Introduction to Modern Network Synthesis, John Wiley & Sons,1960.

[1444] B.J. van Wyk et al. POCS-based graph matching algorithm. IEEE Transactions on PatternAnalysis and Machine Intelligence, Vol. 26(11), pp. 1526–1530, 2004.

[1445] R.G. Vaughan, N.L. Scott, and D.R. White. The Theory of Bandpass Sampling. IEEETransactions Signal Processing, Vol. SP–39, No. 9, pp. 1973–1984, 1991.

[1446] R. Veldhuis. Restoration of Lost Samples in Digital Signals. Prentice Hall, New York,1990.

[1447] R. Venkataramani and Y. Bresler. Sampling theorems for uniform and periodic nonuniformMIMO sampling of multiband signals. IEEE Transactions on Signal Processing, Vol. 51(12),pp. 3152–3163, 2003.

[1448] David Vernon. Fourier Vision - Segmentation and Velocity Measurement Using theFourier Transform. Springer, 2001.

[1449] G.A. Viano. On the extrapolation of optical image data. Journal Math. Phys., Vol. 17,pp. 1160–1165, 1976.

[1450] U. Visitkitjakarn, Wai-Yip Chan, and Yongyi Yang. Recovery of speech spectral parametersusing convex set projection. 1999 IEEE Workshop on Speech Coding Proceedings, pp. 34–36,1999.

[1451] G. Viswanath and T.V. Sreenivas. Cone-kernel representation versus instantaneous powerspectrum. IEEE Transactions on Signal Processing, Vol. 47(1), pp. 250–254, 1999.

[1452] H. Voelker. Toward a unified theory of modulation. Proceedings IEEE, Vol. 54, p. 340, 1966.[1453] L. Vogt. Sampling sums with kernels of finite oscillation. Numer. Funct. Anal., Optimiz., Vol. 9,

pp. 1251–1270, 1987/88.[1454] M. von Laue. Die freiheitsgrade von strahlenbundeln. Ann. Phys., Vol. 44, pp. 1197–1212,

1976.[1455] J.J. Voss. A sampling theorem with nonuniform complex nodes. Journal of Approximation

Theory, Vol. 90(2), pp. 235–254, 1997.

W[1456] L.A. Wainstein and V.D. Zubakov. Extraction of Signals from Noise. Prentice-Hall,

Englewood Cliffs, NJ, 1962.[1457] James S. Walker. Fourier Analysis. Oxford University Press, 1988.[1458] J.F. Walkup. Space-variant coherent optical processing. Optical Engineering, Vol. 19,

pp. 339–346, 1980.[1459] G.G. Walter. A sampling theorem for wavelet subspaces. IEEE Transactions Information

Theory, Vol. 38, pp. 881–884, 1992.[1460] P.T. Walters. Practical applications of inverting spectral turbidity data to provide aerosol size

distributions. Applied Optics, Vol. 19, pp. 2353–2365, 1980.[1461] A. Walther. The question of phase retrieval in optics. Opt. Acta, pp. 41–49, 1962.[1462] A. Walther. Gabor’s theorem and energy transfer through lenses. Journal of the Optical Society

America, Vol. 57, pp. 639–644, 1967.[1463] A. Walther. Radiometry and coherence. Journal of the Optical Society America, Vol. 58,

pp. 1256–1259, 1968.[1464] Danzhi Wang, Li Shujian and Shao Dingrong. The analysis of frequency-hopping signal

acquisition based on Cohen-reassignment joint time-frequency distribution. Proceedings.Asia-Pacific Conference on Environmental Electromagnetics, 2003. CEEM 2003. pp. 21–24,2003.

[1465] J.Y. Wang, P.P. Zhu, X. Zheng X, et al. Study on the inside source hologram reconstructionalgorithm based on discrete Fourier transform Acta Physica Sinica, Vol. 54(3), pp. 1172–1177,2005.

[1466] H.S.C. Wang. On Cauchy’s interpolation formula and sampling theorems. Journal FranklinInstitute, Vol. 289, pp. 233–236, 1970.


REFERENCES 739

[1467] Y. Wang and Q.F. Zhu. Error control and concealment for video communication: A review.Proceedings IEEE Multimedia Signal Processing, pp. 974–997, 1998.

[1468] Q. Wang and L.N. Wu. Translation invariance and sampling theorem of wavelet. IEEETransactions on Signal Processing, Vol. 48(5), pp. 1471–1474, 2000.

[1469] Q. Wang and L.N. Wu. A sampling theorem associated with quasi-fourier transform . IEEETransactions on Signal Processing, Vol. 48(3), pp. 895–895, 2000.

[1470] Yiwei Wang, J.F. Doherty, and R.E. Van Dyck. A POCS-based algorithm to attack imagewatermarks embedded in DFT amplitudes. Proceedings of the 43rd IEEE Midwest Symposiumon Circuits and Systems, 2000. Vol. 3, pp. 1100–1103, 2000.

[1471] G. Watson Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge University Press,Cambridge, 1962.

[1472] H.J. Weaver. Applications of Discrete and Fourier Analysis. Wiley, New York, 1983.[1473] C. Weerasinghe, A. Wee-Chung Liew and Hong Yan. Artifact reduction in compressed images

based on region homogeneity constraints using the projection onto convex sets algorithm.IEEE Transactions on Circuits and Systems for Video Technology, Vol. 12(10), pp. 891–897,2002.

[1474] S.J. Wein. Sampling theorem for the negative exponentially correlated output of lock-inamplifiers. Applied Optics, Vol. 28(20), pp. 4453–4457, 1989.

[1475] A. Weinberg and B. Liu. Discrete time analysis of nonuniform sampling first-and-second orderdigital phase lock loop. IEEE Transactions Communications, pp. 123–137, 1974.

[1476] P. Weiss. Sampling theorems associated with Sturm-Liouville systems. Bull. Amer. Math.Society, Vol. 63, p. 242, 1957.

[1477] P. Weiss. An estimate of the error arising from misapplication of the sampling theorem. Amer.Math. Society Notices 10-351, (Abstract No. 601–54), 1963.

[1478] F. Weisz. Summability of Multi-Dimensional Fourier Series and Hardy Spaces. Springer,2002.

[1479] A.L. Wertheimer and W.L. Wilcock. Light scattering measurements of particle distributions.Applied Optics, Vol. 15, pp. 1616–1620, 1976.

[1480] L.B. White. Signal synthesis from Cohen’s class of bilinear time-frequency signalrepresentations using convex projections. 1991 International Conference on Acoustics,Speech, and Signal Processing, 1991. ICASSP–91. Vol. 3, pp. 2053–2056, 1991.

[1481] Robert White. Chromatography/Fourier Transform Infrared Spectroscopy and itsApplications. CRC, 1989.

[1482] E.T. Whittaker. On the functions which are represented by the expansions of the interpolationtheory. Proceedings Royal Society Edinburgh, Vol. 35, pp. 181–194, 1915.

[1483] E.T. Whittaker and G.N. Watson.A Course of ModernAnalysis. Cambridge University Press,Cambridge, 1927, Chaps. 20 and 21.

[1484] J.M. Whittaker. On the cardinal function of interpolation theory. Proceedings Math. SocietyEdinburgh, Vol. 2, pp. 41–46, 1927–1929.

[1485] J.M. Whittaker. The Fourier theory of the cardinal function. Proceedings Math. SocietyEdinburgh, Vol. 1, pp. 169–176, 1929.

[1486] J.M. Whittaker. Interpolatory Function Theory. Cambridge Tracts in Mathematical Physics,No. 33, Cambridge University Press, Cambridge, 1935.

[1487] G. Whyte and J. Courtial. Experimental demonstration of holographic three-dimensional lightshaping using a Gerchberg-Saxton algorithm. New Journal of Physics. 7 No. 117, 2005.

[1488] Roman Wienands and Wolfgang Joppich. Practical Fourier Analysis for MultigridMethods. Chapman & Hall/CRC, 2004.

[1489] N. Wiener. Extrapolation, Interpolation, and Smoothing of Stationary Time Series. Wileyand Sons Inc., New York, 1949.

[1490] N.Wiener. CollectedWorks,Vol. III (ed. by P.R. Masani). M.I.T. Press, Cambridge, MA., 1981.[1491] E. Wigner. On the quantum correction for thermodynamic equilibrium. Phys. Rev., Vol. 40,

pp. 749–759, 1932.[1492] Howard J. Wilcox and David L. Myers. An Introduction to Lebesgue Integration and

Fourier Series. Dover Publications, 1995.


740 REFERENCES

[1493] R.G. Wiley, H. Schwarzlander, and D.D. Weiner. Demodulation procedure for very widebandFM. IEEE Transactions Commun., Vol. COM–25, pp. 318–327, 1977.

[1494] R.G. Wiley. On an iterative technique for recovery of bandlimited signals. Proceedings IEEE,pp. 522–523, 1978.

[1495] R.G. Wiley. Recovery of bandlimited signals from unequally spaced samples. IEEETransactions Communications, Vol. COM–26, pp. 135–137, 1978.

[1496] Ron R. Williams. Spectroscopy and the Fourier Transform. John Wiley & Sons, 1995.[1497] Earl G. Williams. Fourier Acoustics: Sound Radiation and Nearfield Acoustical

Holography. Academic Press, 1999.[1498] W.J. Williams. Reduced interference distributions: Biological applications and interpretations.

Proceedings of the IEEE. Vol. 84(9), pp. 1264–1280, 1996.[1499] N.P. Willis and Y. Bresler. Norm invariance of minimax interpolation IEEE Transactions

Information Theory, Vol. 38, No. 3, pp. 1177–1181, 1992.[1500] T. Wilson and C. Sheppard. Theory and Practice of Scanning Microscopy. Academic Press,

London, 1978.[1501] Steve Winder. Analog and Digital Filter Design, Second Edition, Newnes, 2002.[1502] D.J. Wingham. The reconstruction of a band-limited function and its Fourier transform from

a finite number of samples at arbitrary locations by singular value decomposition. IEEETransactions Signal Processing, Vol. SP–40, pp. 559–570, 1992.

[1503] J.T. Winthrop. Propagation of structural information in optical wave fields. Journal of theOptical Society America, Vol. 61, pp. 15–30, 1971.

[1504] E. Wolf. Coherence and radiometry. Journal of the Optical Society America, Vol. 68, pp. 6–17,1982.

[1505] E. Wolf. New theory of partial coherence in the space-frequency domain. Part I: Spectraand cross spectra of steady-state sources. Journal of the Optical Society America, Vol. 72,pp. 343–351, 1982.

[1506] E. Wolf. Coherent-mode propagation in spatially bandlimited wave fields. Journal of theOptical Society America A, Vol. 3, pp. 1920–1924, 1986.

[1507] H. Wolter. Zum grundtheorem der informationstheorie, insbesondere in der optik. Physica,pp. 457–475, 1958.

[1508] H. Wolter. On basic analogies and principal differences between optical and electronicinformation. In Progress in Optics, E. Wolf, editor. North-Holland,Amsterdam, pp. 155–210,1961.

[1509] John W. Woods. Multidimensional Signal, Image, and Video Processing and Coding.Academic Press, 2006.

[1510] P.M. Woodward. Probability and Information Theory with Applications to Radar.Pergamon Press Ltd., London, 1953.

[1511] C.R. Worthington. Sampling theorem expressions in membrane diffraction. Journal of AppliedCrystallography, Vol. 21, Part 4, pp. 322–325, 1988.

[1512] E.G. Woschni. Braking the sampling theorem and its consequences. Annalen der Physik,Vol. 43(3–5), pp. 390–396, 1986.

[1513] J.M. Wozencraft and I.M. Jacobs. Principles of Communication Engineering. John Wiley &Sons, Inc., New York, 1965.

[1514] J.S. Wu and J.C.H. Spence. Phase extension in crystallography using the iterative Fienup-Gerchberg-Saxton algorithm and Hilbert transforms. Acta Crystallographica, Section A.59, pp. 577–583, Part 6 2003.

[1515] W.C.S. Wu, Kwan F. Cheung and R.J. Marks II. Multidimensional Projection Window. IEEETransactions on Circuits and Systems, Vol. 35, No. 9, pp. 1168–1172, 1988.

X[1516] X. Xia and Z. Zhang. A note on difference methods for the prediction of band-limited signals

from past samples. IEEE Transactions Information Theory, Vol. IT–37, No. 6, pp. 1662–1665,1991.


REFERENCES 741

[1517] X.G. Xia and Z.Zhang.On sampling theorem, wavelets and wavelet transforms. IEEETransactions on Signal Processing, Vol. 41(12), pp. 3524–3535, 1993.

[1518] Xg Xia. Extentions of the Papoulis-Gerchberg algorithm for analytic functions. Journal ofMathematical Analysis and Applications, Vol. 179(1), pp. 187–202, 1993.

[1519] Xiang-Gen Xia. On bandlimited signals with fractional Fourier transform. IEEE SignalProcessing Letters, Vol. 3(3), pp. 72–74, 1996.

[1520] J. Xian and W. Lin, Sampling and reconstruction in time-warped spaces and their applications.Applied Mathematics and Computation, Vol. 157(1), pp. 153–173, 27, 2004.

[1521] Zelong Xiao, Jianzhong Xu, Shusheng Peng and Shanxiang Mou. Super-Resolution ImageRestoration of a PMMW Sensor Based on POCS Algorithm 1st International Symposium onSystems and Control in Aerospace and Astronautics, 2006. ISSCAA 2006. pp. 680–683, 2006.

[1522] Gang Xiong, Zhao Hui-chang, Wang Li-Jun and Liu Ji-Bin. The wide sense time-frequencyrepresentation based on the wavelet and its relation with Cohen’s class. ICMMT 4thInternational Conference on, Proceedings Microwave and Millimeter Wave Technology, 2004.pp. 677–680, 2004.

[1523] C.Y. Xu, F. Kamalabadi, and S.A. Boppart. Comparative performance analysis of time-frequency distributions for spectroscopic optical coherence tomography. Applied Optics,Vol. 44(10), pp. 1813–1822, 2005.

Y[1524] A.D.Yaghjian. Simplified approach to probe-corrected spherical near-field scanning. Electron.

Letters, Vol. 20, pp. 195–196, 1984.[1525] A.D. Yaghjian. Antenna coupling and near-field sampling in plane-polar cordinates. IEEE

Transactions Antennas & Propagation, Vol. 40, pp. 304–312, 1992.[1526] M. Yamaguchi, N. Ohyama, T. Honda, J. Tsujiuchi, and S. Hiratsuka. A color image sampling

method with suppression of Moiré fringes. Optical Communication, Vol. 69, pp. 349–352,1989.

[1527] H. Yan and J.T. Mao. The realation of low-frequency restoration methods to the Gerchberg-Papoulis algorithm. Magnetic Resonance in Medicine, Vol. 16(1), pp. 166–172, 1990.

[1528] M. Yanagida and O. Kakusho. Generalized sampling theorem and its application by uniformsampling. Electronics & Communications in Japan, Vol. 57(11), pp. 42–49, 1974.

[1529] G. Yang and B. Shi. A time-frequency distribution based on a moving and combined kerneland its application in the fault diagnosis of rotating machinery. Key Engineering Materials.245–2, pp. 183–190, 2003.

[1530] G.G. Yang and E. Leith. An image deblurring method using diffraction gratings. OpticalCommunication, Vol. 36, pp. 101–106, 1981.

[1531] G.Z. Yang, B.Z. Dong, et al. Gerchberg-Saxton and Yang-Gu algorithms for phase retrievalin a nonunitary transform system - a comparison. Applied Optics, Vol. 33(2), pp. 209–218,1994.

[1532] S.Z.Yang, Z.X. Cheng, andY.Y. Tang.Approximate sampling theorem for bivariate continuousfunction. Applied Mathematics and Mechanics - English Edition, Vol. 24(11), pp. 1355–1361,2003.

[1533] Y. Yang, N.P. Galatsanos, and A. K. Katsaggelos. Projection-Based Spatially-AdaptiveReconstruction of Block Transform Compressed Images. IEEE Transactions on ImageProcessing, Vol. 4, No. 7, pp. 896–908, 1995.

[1534] Y. Yang and N.P. Galatsanos. Removal of compression artifacts using projections ontoconvex sets and line process modeling. IEEE Transactions Image Processing, Vol. 10(6),pp. 1345–1357, 1997.

[1535] Yongyi Yang, N.P. Galatsanos. Removal of compression artifacts using projections ontoconvex sets and line process modeling. IEEE Transactions on Image Processing, Vol. 6(10),pp. 1345–1357, 1997.

[1536] K. Yao. On some representations and sampling expansions for bandlimited signals. Ph.D.thesis, Dept. of Electrical Engineering, Princeton University, Princeton, NJ, 1965.


742 REFERENCES

[1537] K. Yao. Applications of reproducing kernel Hilbert spaces – Bandlimited signal models.Information & Control, Vol. 11, pp. 429–444, 1967.

[1538] K. Yao and J.B. Thomas. On truncation error bounds for sampling representations ofbandlimited signals. IEEE Transactions Aerospace & Electronic Systems, Vol. AES–2, p. 640,1966.

[1539] K. Yao and J.B. Thomas. On some stability and interpolating properties of nonuniformsampling expansions. IEEE Transactions Circuit Theory, Vol. CT–14, pp. 404–408, 1967.

[1540] K. Yao and J.B. Thomas. On a class of nonuniform sampling representation. Symp. SignalTransactions Processing (Columbia Univ.), 1968.

[1541] B. Yegnanarayana, S. Tanveer Fatima, B.T.K.R. Nehru, and B. Venkataramanan. Significanceof initial interpolation in bandlimited signal interpolation. IEEE Transactions Acoust., Speech,Signal Processing, Vol. ASSP-37, No. 1, pp. 151–152, 1989.

[1542] Shu-jen Yeh and Henry Stark. Iterative and one-step reconstruction from nonuniform samplesby convex projections. Journal of the Optical Society America A, Vol. 7, No. 3, pp. 491–499,1990.

[1543] Shu-jeh Yeh and Henry Stark. Learning in neural nets using projection methods. OpticalComputing and Processing, Vol. 1, No. 1, pp. 47–59, 1991.

[1544] J.L. Yen. On the nonuniform sampling of bandwidth limited signals. IRE Transactions CircuitTheory, Vol. CT–3, pp. 251–257, 1956.

[1545] J.L. Yen. On the synthesis of line sources and infinite strip sources. IRE TransactionsAntennas & Propagation, pp. 40–46, 1957.

[1546] I. Samil Yetik and A. Nehorai. Beamforming using the fractional Fourier transform. IEEETransactions on Signal Processing, Vol. 51(6), pp. 1663–1668, 2003.

[1547] Changboon Yim and Nam Ik Cho. Blocking artifact reduction method based on non-iterativePOCS in the DCT domain. ICIP 2005, IEEE International Conference on Image Processing,Vol. 2, pp. 11–14, 2005.

[1548] H. Yoshida and S. Takata. The growth of Fourier’s theory of heat conduction and hisexperimental study. Historia Sci., (2) 1 (1), pp. 1–26, 1991.

[1549] D.C. Youla. Generalized image restoration by method of alternating orthogonal projections.IEEE Transactions Circuits & Systems, Vol. CAS–25, pp. 694–702, 1978.

[1550] D.C. Youla and H. Webb. Image restoration by the method of convex projection: Part 1 -theory. IEEE Transactions Medical Imaging, Vol. MI–1, pp. 81–94, 1982.

[1551] D.C. Youla. In Image Recovery: Theory and Applications, Mathematical theory of imagerestoration by the method of convex projections, (H. Stark, ed.),Academic Press Inc., Orlando,FL, pp. 29–77, 1987.

[1552] D.C. Youla and V. Velasco. Extensions of a result on the synthesis of signals in the presence ofinconsistent constraints. IEEE Transactions Circuits & Systems, Vol. CAS–33, pp. 465–468,1986.

[1553] Robert M. Young. An Introduction to Nonharmonic Fourier Series. Academic Press;Revised First Ed., 2001.

[1554] F.T.S. Yu. Image restoration, uncertainty, and information. Applied Optics, Vol. 8, pp. 53–58,1969.

[1555] F.T.S. Yu. Optical resolving power and physical realizability. Optical Communication, Vol. 1,pp. 319–322, 1970.

[1556] F.T.S. Yu. Coherent and digital image enhancement, their basic differences and constraints.Optical Communication, Vol. 3, pp. 440–442, 1971.

[1557] Gong-San Yu et al. POCS-based error concealment for packet video using multiframe overlapinformation. IEEE Transactions on Circuits and Systems for Video Technology, Vol. 8(4),pp. 422–434, 1998.

[1558] Li Yu, Kuan-Quan Wang, Cheng-Fa Wang and D. Zhang. Iris verification based on fractionalFourier transform. Proceedings. 2002 International Conference on Machine Learning andCybernetics, 2002. Vol. 3, pp. 1470–1473, 2002.

[1559] E. Yudilevich and H. Stark. Interpolation from samples on a linear spiral scan. IEEETransactions Medical Imaging, Vol. MI–6, pp. 193–200, 1987.


REFERENCES 743

[1560] E. Yudilevich and H. Stark. Spiral sampling: Theory and application to magnetic resonanceimaging, Journal of the Optical Society America A, Vol. 5, pp. 542–553, 1988.

Z[1561] L.A. Zadeh. A general theory of linear signal transmission systems, Journal Franklin Institute,

Vol. 253, pp. 293–312, 1952.[1562] L.A. Zadeh. Fuzzy sets. Information and Control, Vol. 8, pp. 338–353, 1965; reprinted in

J.C. Bezdek, editor, Fuzzy Models for Pattern Recognition, IEEE Press, 1992.[1563] Samy Zafrany. Fourier Series and Integral Transforms. Cambridge University Press, 1997.[1564] J. Zak. Finite translations in solid-state physics. Phys. Rev. Letters, Vol. 19, pp. 1385–1387,

1967.[1565] J. Zak. Dynamics of electrons in solids in external fields. Phys. Rev., Vol. 168, pp. 686–695,

1968.[1566] J. Zak. The kq-representation in the dynamics of electrons in solids. Solid State Physics,

Vol. 27, pp. 1–62, 1972.[1567] M. Zakai. Band-limited functions and the sampling theorem. Information & Control, Vol. 8,

pp. 143–158, 1965.[1568] A. Zakhor. Sampling schemes for reconstruction of multidimensional signals from multiple

level threshold crossing. In Proceedings ICASSP ’88, 1988.[1569] A. Zakhor, R. Weisskoff, and R. Rzedzian. Optimal sampling and reconstruction of MRI

signals resulting from sinusoidal gradients. IEEE Transactions Signal Processing, Vol. SP–39,No. 9, pp. 2056–2065, 1988.

[1570] Z. Zalevsky, D. Mendlovic and R.G. Dorsch. Gerchberg-Saxton algorithm applied in thefractional Fourier or the Fresnel domain. Optics Letters, Vol. 21(12), pp. 842–844, 1996.

[1571] H. Zander. Fundamentals and methods of digital audio technology. II. Sampling process.Fernseh- und Kino-Tech., Vol. 38, pp. 333–338, 1984.

[1572] Ahmed I. Zayed. Sampling expansion for the continuous Bessel transform. Applied Anal.,Vol. 27, pp. 47–65, 1988.

[1573] Ahmed I. Zayed, G. Hinsen, and P. Butzer. On Lagrange interpolation and Kramer-typesampling theorems associated with Sturm-Liouville problems. SIAM Journal Applied Math,Vol. 50, No. 3, pp. 893–909, 1990.

[1574] Ahmed I. Zayed, M.A. Elsayed, and M.H. Annaby. On Lagrange interpolations andKramer sampling theorem associated with self-adjoint boundary-value problems. Journalof Mathematical Analysis and Applications, Vol. 158(1), pp. 269–284, 1991.

[1575] Ahmed I. Zayed. On Kramer sampling theorem associated with general Strum-Liouvilleproblems and Largange interpolation. SIAM J. on Applied Mathematics, Vol. 51(2), pp. 575–604, 1991.

[1576] Ahmed I. Zayed. Kramer sampling theorem for multidimensional signals and its relationshipwith Largrange - type interpolations. Multidimensional Systems and Signal Processing,Vol. 3(4), pp. 323–340, 1992.

[1577] Ahmed I. Zayed. Advances in Shannon’s Sampling Theory. CRC, 1993.[1578] Ahmed I. Zayed. A sampling theorem for signals band-limited to a general domain in several

dimensions. Journal of Mathematical Analysis and Applications, Vol. 187(1), pp. 196–211,1994.

[1579] Ahmed I. Zayed. On the relationship between the Fourier and fractional Fourier transforms.IEEE Signal Processing Letters, Vol. 3(12), pp. 310–311, 1996.

[1580] Ahmed I. Zayed and A.G. Garcia. Sampling theorem associated with a Dirac operator and theHartley transform. Journal of Mathematical Analysis and Applications, Vol. 214(2), pp. 587–598, 1997.

[1581] Ahmed I. Zayed. Hilbert transform associated with the fractional Fourier transform. IEEESignal Processing Letters, Vol. 5(8), pp. 206–208, 1998.

[1582] A.H. Zemanian. Distribution Theory and Transform Analysis. McGraw-Hill, New York,1965.

[1583] A.H. Zemanian. Generalized Integral Transforms. Interscience, New York, 1968.


744 REFERENCES

[1584] Bilin Zhang, Shunsuke Sato, and P.C. Ching. Speech signal processing using a time-frequencydistribution of Cohen’s class. Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, pp. 624–627, 1994.

[1585] B. Zhang and S. Sato. A time-frequency distribution of Cohen’s class with a compound kerneland its application to speech signal processing. IEEE Transactions on Signal Processing,Vol. 42(1), pp. 54–64, 1994.

[1586] C. Zhao and P. Zhao. Sampling theorem and irregular sampling theorem for multiwaveletsubspaces. IEEE Transactions on Signal Processing, Vol. 53(2), pp. 705–713, Part 1, 2005.

[1587] Yunxin Zhao, L.E. Atlas and R.J. Marks II. The use of cone-shape kernels for generalizedtime-frequency representations of nonstationary signals. IEEE Transactions on Acoustics,Speech and Signal Processing, Vol. 38, pp. 1084–1091, 1990.

[1588] Di Zhang and Minghui Du. High-resolution image reconstruction using joint constrainededge pattern recognition and POCS formulation. Control, Automation, Robotics and VisionConference, 2004. Vol. 2, 6–9, pp. 832–837, 2004.

[1589] G.T. Zheng, P.D. McFadden. A time-frequency distribution for analysis of signals withtransient components and its application to vibration analysis. Journal of Vibration andAcoustics – Transactions of the ASME. Vol. 121(3), pp. 328–333, 1999.

[1590] L. Zhizhiashvili. Trigonometric Fourier Series and their Conjugates. Springer, 1996.[1591] X.W. Zhou and W.C. Sun. On the sampling theorem for wavelet subspaces. Journal of Fourier

Analysis and Applications, Vol. 5(4), pp. 347–354, 1999.[1592] X.W. Zhou and W.C. Sun. An aspect of the sampling theorem. International Journal of

Wavelets, Multiresolution and Information Processing, Vol. 3(2), pp. 247–255, 2005.[1593] Y.M. Zhu. Generalized sampling theorem. IEEETransactions on Circuits and Systems -Analog

and Digital Signal Processing, Vol. 39(8), pp. 587–588, 1992.[1594] Yang-Ming Zhu, Zhi-Zhong Wang, and Yu Wei. A convex projections approach to spectral

analysis. IEEE Transactions on Signal Processing, Vol. 42(5), pp. 1284–1287, May 1994.[1595] Anders E. Zonst. Understanding the FFT, Second Edition. Revised. Citrus Press, 2000.[1596] Ju Jia Zou and Hong Yan. A deblocking method for BDCT compressed images based on

adaptive projections. IEEE Transactions on Circuits and Systems for Video Technology,Vol. 15(3), pp. 430–435, 2005.

[1597] S. Zozor and P.O. Amblard. Stochastic Resonance in Discrete Time Nonlinear AR(1) Models.IEEE Transactions on Signal Processing, Vol. 47, No. 1, pp. 108–122, 1999.

[1598] Gary Zukav, Dancing Wu Li Masters: An Overview of the New Physics. Harper PerennialModern Classics, 2001.

handbook of fourier analysis & its applicationsthe nonuniform discrete fourier transform and its...

Documents